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Simplifying 5(x + -18 + -4) * x = -36 Reorder the terms: 5(-18 + -4 + x) * x = -36 Combine like terms: -18 + -4 = -22 5(-22 + x) * x = -36 Reorder the terms for easier multiplication: 5x(-22 + x) = -36 (-22 * 5x + x * 5x) = -36 (-110x + 5x2) = -36 Solving -110x + 5x2 = -36 Solving for variable 'x'. Reorder the terms: 36 + -110x + 5x2 = -36 + 36 Combine like terms: -36 + 36 = 0 36 + -110x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.2 + -22x + x2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + -22x + -7.2 + x2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + -22x + x2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + -22x + x2 = 0 + -7.2 -22x + x2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 -22x + x2 = -7.2 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -7.2 + 121 Reorder the terms: 121 + -22x + x2 = -7.2 + 121 Combine like terms: -7.2 + 121 = 113.8 121 + -22x + x2 = 113.8 Factor a perfect square on the left side: (x + -11)(x + -11) = 113.8 Calculate the square root of the right side: 10.667708282 Break this problem into two subproblems by setting (x + -11) equal to 10.667708282 and -10.667708282.Subproblem 1
x + -11 = 10.667708282 Simplifying x + -11 = 10.667708282 Reorder the terms: -11 + x = 10.667708282 Solving -11 + x = 10.667708282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 10.667708282 + 11 Combine like terms: -11 + 11 = 0 0 + x = 10.667708282 + 11 x = 10.667708282 + 11 Combine like terms: 10.667708282 + 11 = 21.667708282 x = 21.667708282 Simplifying x = 21.667708282Subproblem 2
x + -11 = -10.667708282 Simplifying x + -11 = -10.667708282 Reorder the terms: -11 + x = -10.667708282 Solving -11 + x = -10.667708282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -10.667708282 + 11 Combine like terms: -11 + 11 = 0 0 + x = -10.667708282 + 11 x = -10.667708282 + 11 Combine like terms: -10.667708282 + 11 = 0.332291718 x = 0.332291718 Simplifying x = 0.332291718Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.667708282, 0.332291718}
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