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Simplifying 400 = 2x(5 + x) 400 = (5 * 2x + x * 2x) 400 = (10x + 2x2) Solving 400 = 10x + 2x2 Solving for variable 'x'. Reorder the terms: 400 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 400 + -10x + -2x2 = 0 + 2x2 + -2x2 400 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 400 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(200 + -5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(200 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 200 + -5x + -1x2 = 0 Solving 200 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200 + 5x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 5x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 5x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 5x + x2 = 0 + 200 5x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 5x + x2 = 200 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 200 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 200 + 6.25 Combine like terms: 200 + 6.25 = 206.25 6.25 + 5x + x2 = 206.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 206.25 Calculate the square root of the right side: 14.361406616 Break this problem into two subproblems by setting (x + 2.5) equal to 14.361406616 and -14.361406616.Subproblem 1
x + 2.5 = 14.361406616 Simplifying x + 2.5 = 14.361406616 Reorder the terms: 2.5 + x = 14.361406616 Solving 2.5 + x = 14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 14.361406616 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 14.361406616 + -2.5 x = 14.361406616 + -2.5 Combine like terms: 14.361406616 + -2.5 = 11.861406616 x = 11.861406616 Simplifying x = 11.861406616Subproblem 2
x + 2.5 = -14.361406616 Simplifying x + 2.5 = -14.361406616 Reorder the terms: 2.5 + x = -14.361406616 Solving 2.5 + x = -14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -14.361406616 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -14.361406616 + -2.5 x = -14.361406616 + -2.5 Combine like terms: -14.361406616 + -2.5 = -16.861406616 x = -16.861406616 Simplifying x = -16.861406616Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.861406616, -16.861406616}Solution
x = {11.861406616, -16.861406616}
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