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Simplifying (8x + -10) * 7x = 180 Reorder the terms: (-10 + 8x) * 7x = 180 Reorder the terms for easier multiplication: 7x(-10 + 8x) = 180 (-10 * 7x + 8x * 7x) = 180 (-70x + 56x2) = 180 Solving -70x + 56x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -70x + 56x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -70x + 56x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + -35x + 28x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + -35x + 28x2)' equal to zero and attempt to solve: Simplifying -90 + -35x + 28x2 = 0 Solving -90 + -35x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -3.214285714 + -1.25x + x2 = 0 Move the constant term to the right: Add '3.214285714' to each side of the equation. -3.214285714 + -1.25x + 3.214285714 + x2 = 0 + 3.214285714 Reorder the terms: -3.214285714 + 3.214285714 + -1.25x + x2 = 0 + 3.214285714 Combine like terms: -3.214285714 + 3.214285714 = 0.000000000 0.000000000 + -1.25x + x2 = 0 + 3.214285714 -1.25x + x2 = 0 + 3.214285714 Combine like terms: 0 + 3.214285714 = 3.214285714 -1.25x + x2 = 3.214285714 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 3.214285714 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 3.214285714 + 0.390625 Combine like terms: 3.214285714 + 0.390625 = 3.604910714 0.390625 + -1.25x + x2 = 3.604910714 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 3.604910714 Calculate the square root of the right side: 1.898660242 Break this problem into two subproblems by setting (x + -0.625) equal to 1.898660242 and -1.898660242.Subproblem 1
x + -0.625 = 1.898660242 Simplifying x + -0.625 = 1.898660242 Reorder the terms: -0.625 + x = 1.898660242 Solving -0.625 + x = 1.898660242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.898660242 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.898660242 + 0.625 x = 1.898660242 + 0.625 Combine like terms: 1.898660242 + 0.625 = 2.523660242 x = 2.523660242 Simplifying x = 2.523660242Subproblem 2
x + -0.625 = -1.898660242 Simplifying x + -0.625 = -1.898660242 Reorder the terms: -0.625 + x = -1.898660242 Solving -0.625 + x = -1.898660242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.898660242 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.898660242 + 0.625 x = -1.898660242 + 0.625 Combine like terms: -1.898660242 + 0.625 = -1.273660242 x = -1.273660242 Simplifying x = -1.273660242Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.523660242, -1.273660242}Solution
x = {2.523660242, -1.273660242}
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