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Simplifying 25x(32 + -1x) * 5 = 400 Reorder the terms for easier multiplication: 25 * 5x(32 + -1x) = 400 Multiply 25 * 5 125x(32 + -1x) = 400 (32 * 125x + -1x * 125x) = 400 (4000x + -125x2) = 400 Solving 4000x + -125x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 4000x + -125x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 4000x + -125x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(-16 + 160x + -5x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-16 + 160x + -5x2)' equal to zero and attempt to solve: Simplifying -16 + 160x + -5x2 = 0 Solving -16 + 160x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3.2 + -32x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -32x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -32x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -32x + x2 = 0 + -3.2 -32x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -32x + x2 = -3.2 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -3.2 + 256 Reorder the terms: 256 + -32x + x2 = -3.2 + 256 Combine like terms: -3.2 + 256 = 252.8 256 + -32x + x2 = 252.8 Factor a perfect square on the left side: (x + -16)(x + -16) = 252.8 Calculate the square root of the right side: 15.899685531 Break this problem into two subproblems by setting (x + -16) equal to 15.899685531 and -15.899685531.Subproblem 1
x + -16 = 15.899685531 Simplifying x + -16 = 15.899685531 Reorder the terms: -16 + x = 15.899685531 Solving -16 + x = 15.899685531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 15.899685531 + 16 Combine like terms: -16 + 16 = 0 0 + x = 15.899685531 + 16 x = 15.899685531 + 16 Combine like terms: 15.899685531 + 16 = 31.899685531 x = 31.899685531 Simplifying x = 31.899685531Subproblem 2
x + -16 = -15.899685531 Simplifying x + -16 = -15.899685531 Reorder the terms: -16 + x = -15.899685531 Solving -16 + x = -15.899685531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -15.899685531 + 16 Combine like terms: -16 + 16 = 0 0 + x = -15.899685531 + 16 x = -15.899685531 + 16 Combine like terms: -15.899685531 + 16 = 0.100314469 x = 0.100314469 Simplifying x = 0.100314469Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.899685531, 0.100314469}Solution
x = {31.899685531, 0.100314469}
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