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Simplifying -4x(x + 6) + 165 = 5x + -9(x + -9) Reorder the terms: -4x(6 + x) + 165 = 5x + -9(x + -9) (6 * -4x + x * -4x) + 165 = 5x + -9(x + -9) (-24x + -4x2) + 165 = 5x + -9(x + -9) Reorder the terms: 165 + -24x + -4x2 = 5x + -9(x + -9) Reorder the terms: 165 + -24x + -4x2 = 5x + -9(-9 + x) 165 + -24x + -4x2 = 5x + (-9 * -9 + x * -9) 165 + -24x + -4x2 = 5x + (81 + -9x) Reorder the terms: 165 + -24x + -4x2 = 81 + 5x + -9x Combine like terms: 5x + -9x = -4x 165 + -24x + -4x2 = 81 + -4x Solving 165 + -24x + -4x2 = 81 + -4x Solving for variable 'x'. Reorder the terms: 165 + -81 + -24x + 4x + -4x2 = 81 + -4x + -81 + 4x Combine like terms: 165 + -81 = 84 84 + -24x + 4x + -4x2 = 81 + -4x + -81 + 4x Combine like terms: -24x + 4x = -20x 84 + -20x + -4x2 = 81 + -4x + -81 + 4x Reorder the terms: 84 + -20x + -4x2 = 81 + -81 + -4x + 4x Combine like terms: 81 + -81 = 0 84 + -20x + -4x2 = 0 + -4x + 4x 84 + -20x + -4x2 = -4x + 4x Combine like terms: -4x + 4x = 0 84 + -20x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(21 + -5x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(21 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 21 + -5x + -1x2 = 0 Solving 21 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + 5x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 5x + x2 = 0 + 21 5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 5x + x2 = 21 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 = 21 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 21 + 6.25 Combine like terms: 21 + 6.25 = 27.25 6.25 + 5x + x2 = 27.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 2.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 2.5 = 5.220153254 Simplifying x + 2.5 = 5.220153254 Reorder the terms: 2.5 + x = 5.220153254 Solving 2.5 + x = 5.220153254 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 = 5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.220153254 + -2.5 x = 5.220153254 + -2.5 Combine like terms: 5.220153254 + -2.5 = 2.720153254 x = 2.720153254 Simplifying x = 2.720153254Subproblem 2
x + 2.5 = -5.220153254 Simplifying x + 2.5 = -5.220153254 Reorder the terms: 2.5 + x = -5.220153254 Solving 2.5 + x = -5.220153254 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 = -5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.220153254 + -2.5 x = -5.220153254 + -2.5 Combine like terms: -5.220153254 + -2.5 = -7.720153254 x = -7.720153254 Simplifying x = -7.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.720153254, -7.720153254}Solution
x = {2.720153254, -7.720153254}
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