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Simplifying (2x + -32)(2x + 16) = 924 Reorder the terms: (-32 + 2x)(2x + 16) = 924 Reorder the terms: (-32 + 2x)(16 + 2x) = 924 Multiply (-32 + 2x) * (16 + 2x) (-32(16 + 2x) + 2x * (16 + 2x)) = 924 ((16 * -32 + 2x * -32) + 2x * (16 + 2x)) = 924 ((-512 + -64x) + 2x * (16 + 2x)) = 924 (-512 + -64x + (16 * 2x + 2x * 2x)) = 924 (-512 + -64x + (32x + 4x2)) = 924 Combine like terms: -64x + 32x = -32x (-512 + -32x + 4x2) = 924 Solving -512 + -32x + 4x2 = 924 Solving for variable 'x'. Reorder the terms: -512 + -924 + -32x + 4x2 = 924 + -924 Combine like terms: -512 + -924 = -1436 -1436 + -32x + 4x2 = 924 + -924 Combine like terms: 924 + -924 = 0 -1436 + -32x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-359 + -8x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-359 + -8x + x2)' equal to zero and attempt to solve: Simplifying -359 + -8x + x2 = 0 Solving -359 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '359' to each side of the equation. -359 + -8x + 359 + x2 = 0 + 359 Reorder the terms: -359 + 359 + -8x + x2 = 0 + 359 Combine like terms: -359 + 359 = 0 0 + -8x + x2 = 0 + 359 -8x + x2 = 0 + 359 Combine like terms: 0 + 359 = 359 -8x + x2 = 359 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 359 + 16 Reorder the terms: 16 + -8x + x2 = 359 + 16 Combine like terms: 359 + 16 = 375 16 + -8x + x2 = 375 Factor a perfect square on the left side: (x + -4)(x + -4) = 375 Calculate the square root of the right side: 19.364916731 Break this problem into two subproblems by setting (x + -4) equal to 19.364916731 and -19.364916731.Subproblem 1
x + -4 = 19.364916731 Simplifying x + -4 = 19.364916731 Reorder the terms: -4 + x = 19.364916731 Solving -4 + x = 19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 19.364916731 + 4 Combine like terms: -4 + 4 = 0 0 + x = 19.364916731 + 4 x = 19.364916731 + 4 Combine like terms: 19.364916731 + 4 = 23.364916731 x = 23.364916731 Simplifying x = 23.364916731Subproblem 2
x + -4 = -19.364916731 Simplifying x + -4 = -19.364916731 Reorder the terms: -4 + x = -19.364916731 Solving -4 + x = -19.364916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -19.364916731 + 4 Combine like terms: -4 + 4 = 0 0 + x = -19.364916731 + 4 x = -19.364916731 + 4 Combine like terms: -19.364916731 + 4 = -15.364916731 x = -15.364916731 Simplifying x = -15.364916731Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.364916731, -15.364916731}Solution
x = {23.364916731, -15.364916731}
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