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Simplifying 600 = (10 + 2x)(20 + 2x) + -200 Multiply (10 + 2x) * (20 + 2x) 600 = (10(20 + 2x) + 2x * (20 + 2x)) + -200 600 = ((20 * 10 + 2x * 10) + 2x * (20 + 2x)) + -200 600 = ((200 + 20x) + 2x * (20 + 2x)) + -200 600 = (200 + 20x + (20 * 2x + 2x * 2x)) + -200 600 = (200 + 20x + (40x + 4x2)) + -200 Combine like terms: 20x + 40x = 60x 600 = (200 + 60x + 4x2) + -200 Reorder the terms: 600 = 200 + -200 + 60x + 4x2 Combine like terms: 200 + -200 = 0 600 = 0 + 60x + 4x2 600 = 60x + 4x2 Solving 600 = 60x + 4x2 Solving for variable 'x'. Reorder the terms: 600 + -60x + -4x2 = 60x + -60x + 4x2 + -4x2 Combine like terms: 60x + -60x = 0 600 + -60x + -4x2 = 0 + 4x2 + -4x2 600 + -60x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 600 + -60x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(150 + -15x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(150 + -15x + -1x2)' equal to zero and attempt to solve: Simplifying 150 + -15x + -1x2 = 0 Solving 150 + -15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -150 + 15x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + 15x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 15x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 15x + x2 = 0 + 150 15x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 15x + x2 = 150 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 150 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 150 + 56.25 Combine like terms: 150 + 56.25 = 206.25 56.25 + 15x + x2 = 206.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 206.25 Calculate the square root of the right side: 14.361406616 Break this problem into two subproblems by setting (x + 7.5) equal to 14.361406616 and -14.361406616.Subproblem 1
x + 7.5 = 14.361406616 Simplifying x + 7.5 = 14.361406616 Reorder the terms: 7.5 + x = 14.361406616 Solving 7.5 + x = 14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 14.361406616 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 14.361406616 + -7.5 x = 14.361406616 + -7.5 Combine like terms: 14.361406616 + -7.5 = 6.861406616 x = 6.861406616 Simplifying x = 6.861406616Subproblem 2
x + 7.5 = -14.361406616 Simplifying x + 7.5 = -14.361406616 Reorder the terms: 7.5 + x = -14.361406616 Solving 7.5 + x = -14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -14.361406616 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -14.361406616 + -7.5 x = -14.361406616 + -7.5 Combine like terms: -14.361406616 + -7.5 = -21.861406616 x = -21.861406616 Simplifying x = -21.861406616Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.861406616, -21.861406616}Solution
x = {6.861406616, -21.861406616}
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