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Simplifying 64 = (20 + 2x)(10 + 2x) Multiply (20 + 2x) * (10 + 2x) 64 = (20(10 + 2x) + 2x * (10 + 2x)) 64 = ((10 * 20 + 2x * 20) + 2x * (10 + 2x)) 64 = ((200 + 40x) + 2x * (10 + 2x)) 64 = (200 + 40x + (10 * 2x + 2x * 2x)) 64 = (200 + 40x + (20x + 4x2)) Combine like terms: 40x + 20x = 60x 64 = (200 + 60x + 4x2) Solving 64 = 200 + 60x + 4x2 Solving for variable 'x'. Combine like terms: 64 + -200 = -136 -136 + -60x + -4x2 = 200 + 60x + 4x2 + -200 + -60x + -4x2 Reorder the terms: -136 + -60x + -4x2 = 200 + -200 + 60x + -60x + 4x2 + -4x2 Combine like terms: 200 + -200 = 0 -136 + -60x + -4x2 = 0 + 60x + -60x + 4x2 + -4x2 -136 + -60x + -4x2 = 60x + -60x + 4x2 + -4x2 Combine like terms: 60x + -60x = 0 -136 + -60x + -4x2 = 0 + 4x2 + -4x2 -136 + -60x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -136 + -60x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(34 + 15x + x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(34 + 15x + x2)' equal to zero and attempt to solve: Simplifying 34 + 15x + x2 = 0 Solving 34 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + 15x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + 15x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 15x + x2 = 0 + -34 15x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 15x + x2 = -34 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 = -34 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -34 + 56.25 Combine like terms: -34 + 56.25 = 22.25 56.25 + 15x + x2 = 22.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + 7.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + 7.5 = 4.716990566 Simplifying x + 7.5 = 4.716990566 Reorder the terms: 7.5 + x = 4.716990566 Solving 7.5 + x = 4.716990566 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 = 4.716990566 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 4.716990566 + -7.5 x = 4.716990566 + -7.5 Combine like terms: 4.716990566 + -7.5 = -2.783009434 x = -2.783009434 Simplifying x = -2.783009434Subproblem 2
x + 7.5 = -4.716990566 Simplifying x + 7.5 = -4.716990566 Reorder the terms: 7.5 + x = -4.716990566 Solving 7.5 + x = -4.716990566 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 = -4.716990566 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -4.716990566 + -7.5 x = -4.716990566 + -7.5 Combine like terms: -4.716990566 + -7.5 = -12.216990566 x = -12.216990566 Simplifying x = -12.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.783009434, -12.216990566}Solution
x = {-2.783009434, -12.216990566}
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