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Simplifying 8(x2 + -7x) = (2x + 300)(x + -7) + x(3x + 450) Reorder the terms: 8(-7x + x2) = (2x + 300)(x + -7) + x(3x + 450) (-7x * 8 + x2 * 8) = (2x + 300)(x + -7) + x(3x + 450) (-56x + 8x2) = (2x + 300)(x + -7) + x(3x + 450) Reorder the terms: -56x + 8x2 = (300 + 2x)(x + -7) + x(3x + 450) Reorder the terms: -56x + 8x2 = (300 + 2x)(-7 + x) + x(3x + 450) Multiply (300 + 2x) * (-7 + x) -56x + 8x2 = (300(-7 + x) + 2x * (-7 + x)) + x(3x + 450) -56x + 8x2 = ((-7 * 300 + x * 300) + 2x * (-7 + x)) + x(3x + 450) -56x + 8x2 = ((-2100 + 300x) + 2x * (-7 + x)) + x(3x + 450) -56x + 8x2 = (-2100 + 300x + (-7 * 2x + x * 2x)) + x(3x + 450) -56x + 8x2 = (-2100 + 300x + (-14x + 2x2)) + x(3x + 450) Combine like terms: 300x + -14x = 286x -56x + 8x2 = (-2100 + 286x + 2x2) + x(3x + 450) Reorder the terms: -56x + 8x2 = -2100 + 286x + 2x2 + x(450 + 3x) -56x + 8x2 = -2100 + 286x + 2x2 + (450 * x + 3x * x) -56x + 8x2 = -2100 + 286x + 2x2 + (450x + 3x2) Reorder the terms: -56x + 8x2 = -2100 + 286x + 450x + 2x2 + 3x2 Combine like terms: 286x + 450x = 736x -56x + 8x2 = -2100 + 736x + 2x2 + 3x2 Combine like terms: 2x2 + 3x2 = 5x2 -56x + 8x2 = -2100 + 736x + 5x2 Solving -56x + 8x2 = -2100 + 736x + 5x2 Solving for variable 'x'. Reorder the terms: 2100 + -56x + -736x + 8x2 + -5x2 = -2100 + 736x + 5x2 + 2100 + -736x + -5x2 Combine like terms: -56x + -736x = -792x 2100 + -792x + 8x2 + -5x2 = -2100 + 736x + 5x2 + 2100 + -736x + -5x2 Combine like terms: 8x2 + -5x2 = 3x2 2100 + -792x + 3x2 = -2100 + 736x + 5x2 + 2100 + -736x + -5x2 Reorder the terms: 2100 + -792x + 3x2 = -2100 + 2100 + 736x + -736x + 5x2 + -5x2 Combine like terms: -2100 + 2100 = 0 2100 + -792x + 3x2 = 0 + 736x + -736x + 5x2 + -5x2 2100 + -792x + 3x2 = 736x + -736x + 5x2 + -5x2 Combine like terms: 736x + -736x = 0 2100 + -792x + 3x2 = 0 + 5x2 + -5x2 2100 + -792x + 3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 2100 + -792x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(700 + -264x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(700 + -264x + x2)' equal to zero and attempt to solve: Simplifying 700 + -264x + x2 = 0 Solving 700 + -264x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-700' to each side of the equation. 700 + -264x + -700 + x2 = 0 + -700 Reorder the terms: 700 + -700 + -264x + x2 = 0 + -700 Combine like terms: 700 + -700 = 0 0 + -264x + x2 = 0 + -700 -264x + x2 = 0 + -700 Combine like terms: 0 + -700 = -700 -264x + x2 = -700 The x term is -264x. Take half its coefficient (-132). Square it (17424) and add it to both sides. Add '17424' to each side of the equation. -264x + 17424 + x2 = -700 + 17424 Reorder the terms: 17424 + -264x + x2 = -700 + 17424 Combine like terms: -700 + 17424 = 16724 17424 + -264x + x2 = 16724 Factor a perfect square on the left side: (x + -132)(x + -132) = 16724 Calculate the square root of the right side: 129.321305283 Break this problem into two subproblems by setting (x + -132) equal to 129.321305283 and -129.321305283.Subproblem 1
x + -132 = 129.321305283 Simplifying x + -132 = 129.321305283 Reorder the terms: -132 + x = 129.321305283 Solving -132 + x = 129.321305283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '132' to each side of the equation. -132 + 132 + x = 129.321305283 + 132 Combine like terms: -132 + 132 = 0 0 + x = 129.321305283 + 132 x = 129.321305283 + 132 Combine like terms: 129.321305283 + 132 = 261.321305283 x = 261.321305283 Simplifying x = 261.321305283Subproblem 2
x + -132 = -129.321305283 Simplifying x + -132 = -129.321305283 Reorder the terms: -132 + x = -129.321305283 Solving -132 + x = -129.321305283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '132' to each side of the equation. -132 + 132 + x = -129.321305283 + 132 Combine like terms: -132 + 132 = 0 0 + x = -129.321305283 + 132 x = -129.321305283 + 132 Combine like terms: -129.321305283 + 132 = 2.678694717 x = 2.678694717 Simplifying x = 2.678694717Solution
The solution to the problem is based on the solutions from the subproblems. x = {261.321305283, 2.678694717}Solution
x = {261.321305283, 2.678694717}
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