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jennaaanicoleee
 2 years ago
pleasee help!
Solve. x2  8x = 20
What are the solutions of 4x2  3x  5 = 0?
jennaaanicoleee
 2 years ago
pleasee help! Solve. x2  8x = 20 What are the solutions of 4x2  3x  5 = 0?

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JUICEDECAFE
 2 years ago
Best ResponseYou've already chosen the best response.1Simplifying x2 + 8x = 20 Reorder the terms: 8x + x2 = 20 Solving 8x + x2 = 20 Solving for variable 'x'. Reorder the terms: 20 + 8x + x2 = 20 + 20 Combine like terms: 20 + 20 = 0 20 + 8x + x2 = 0 Factor a trinomial. (2 + 1x)(10 + 1x) = 0 Subproblem 1Set the factor '(2 + 1x)' equal to zero and attempt to solve: Simplifying 2 + 1x = 0 Solving 2 + 1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. 2 + 2 + 1x = 0 + 2 Combine like terms: 2 + 2 = 0 0 + 1x = 0 + 2 1x = 0 + 2 Combine like terms: 0 + 2 = 2 1x = 2 Divide each side by '1'. x = 2 Simplifying x = 2 Subproblem 2Set the factor '(10 + 1x)' equal to zero and attempt to solve: Simplifying 10 + 1x = 0 Solving 10 + 1x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. 10 + 10 + 1x = 0 + 10 Combine like terms: 10 + 10 = 0 0 + 1x = 0 + 10 1x = 0 + 10 Combine like terms: 0 + 10 = 10 1x = 10 Divide each side by '1'. x = 10 Simplifying x = 10Solutionx = {2, 10}

JUICEDECAFE
 2 years ago
Best ResponseYou've already chosen the best response.1Simplifying 4x2 + 3x + 5 = 0 Reorder the terms: 5 + 3x + 4x2 = 0 Solving 5 + 3x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. 1.25 + 0.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: 1.25 + 1.25 + 0.75x + x2 = 0 + 1.25 Combine like terms: 1.25 + 1.25 = 0.00 0.00 + 0.75x + x2 = 0 + 1.25 0.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.75x + x2 = 1.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 1.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 1.25 + 0.140625 Combine like terms: 1.25 + 0.140625 = 1.390625 0.140625 + 0.75x + x2 = 1.390625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + 0.375) equal to 1.179247642 and 1.179247642. Subproblem 1x + 0.375 = 1.179247642 Simplifying x + 0.375 = 1.179247642 Reorder the terms: 0.375 + x = 1.179247642 Solving 0.375 + x = 1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. 0.375 + 0.375 + x = 1.179247642 + 0.375 Combine like terms: 0.375 + 0.375 = 0.000 0.000 + x = 1.179247642 + 0.375 x = 1.179247642 + 0.375 Combine like terms: 1.179247642 + 0.375 = 1.554247642 x = 1.554247642 Simplifying x = 1.554247642 Subproblem 2x + 0.375 = 1.179247642 Simplifying x + 0.375 = 1.179247642 Reorder the terms: 0.375 + x = 1.179247642 Solving 0.375 + x = 1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. 0.375 + 0.375 + x = 1.179247642 + 0.375 Combine like terms: 0.375 + 0.375 = 0.000 0.000 + x = 1.179247642 + 0.375 x = 1.179247642 + 0.375 Combine like terms: 1.179247642 + 0.375 = 0.804247642 x = 0.804247642 Simplifying x = 0.804247642 SolutionThe solution to the problem is based on the solutions from the subproblems. x = {1.554247642, 0.804247642}

jennaaanicoleee
 2 years ago
Best ResponseYou've already chosen the best response.0thanks so much you are a lifesaver!
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