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Simplifying 5 = 4(x + -9)(x + -9) Reorder the terms: 5 = 4(-9 + x)(x + -9) Reorder the terms: 5 = 4(-9 + x)(-9 + x) Multiply (-9 + x) * (-9 + x) 5 = 4(-9(-9 + x) + x(-9 + x)) 5 = 4((-9 * -9 + x * -9) + x(-9 + x)) 5 = 4((81 + -9x) + x(-9 + x)) 5 = 4(81 + -9x + (-9 * x + x * x)) 5 = 4(81 + -9x + (-9x + x2)) Combine like terms: -9x + -9x = -18x 5 = 4(81 + -18x + x2) 5 = (81 * 4 + -18x * 4 + x2 * 4) 5 = (324 + -72x + 4x2) Solving 5 = 324 + -72x + 4x2 Solving for variable 'x'. Combine like terms: 5 + -324 = -319 -319 + 72x + -4x2 = 324 + -72x + 4x2 + -324 + 72x + -4x2 Reorder the terms: -319 + 72x + -4x2 = 324 + -324 + -72x + 72x + 4x2 + -4x2 Combine like terms: 324 + -324 = 0 -319 + 72x + -4x2 = 0 + -72x + 72x + 4x2 + -4x2 -319 + 72x + -4x2 = -72x + 72x + 4x2 + -4x2 Combine like terms: -72x + 72x = 0 -319 + 72x + -4x2 = 0 + 4x2 + -4x2 -319 + 72x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -319 + 72x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 79.75 + -18x + x2 = 0 Move the constant term to the right: Add '-79.75' to each side of the equation. 79.75 + -18x + -79.75 + x2 = 0 + -79.75 Reorder the terms: 79.75 + -79.75 + -18x + x2 = 0 + -79.75 Combine like terms: 79.75 + -79.75 = 0.00 0.00 + -18x + x2 = 0 + -79.75 -18x + x2 = 0 + -79.75 Combine like terms: 0 + -79.75 = -79.75 -18x + x2 = -79.75 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -79.75 + 81 Reorder the terms: 81 + -18x + x2 = -79.75 + 81 Combine like terms: -79.75 + 81 = 1.25 81 + -18x + x2 = 1.25 Factor a perfect square on the left side: (x + -9)(x + -9) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -9) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -9 = 1.118033989 Simplifying x + -9 = 1.118033989 Reorder the terms: -9 + x = 1.118033989 Solving -9 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 1.118033989 + 9 Combine like terms: -9 + 9 = 0 0 + x = 1.118033989 + 9 x = 1.118033989 + 9 Combine like terms: 1.118033989 + 9 = 10.118033989 x = 10.118033989 Simplifying x = 10.118033989Subproblem 2
x + -9 = -1.118033989 Simplifying x + -9 = -1.118033989 Reorder the terms: -9 + x = -1.118033989 Solving -9 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -1.118033989 + 9 Combine like terms: -9 + 9 = 0 0 + x = -1.118033989 + 9 x = -1.118033989 + 9 Combine like terms: -1.118033989 + 9 = 7.881966011 x = 7.881966011 Simplifying x = 7.881966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.118033989, 7.881966011}
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