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Simplifying 5x(x + -8) = 172 Reorder the terms: 5x(-8 + x) = 172 (-8 * 5x + x * 5x) = 172 (-40x + 5x2) = 172 Solving -40x + 5x2 = 172 Solving for variable 'x'. Reorder the terms: -172 + -40x + 5x2 = 172 + -172 Combine like terms: 172 + -172 = 0 -172 + -40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -34.4 + -8x + x2 = 0 Move the constant term to the right: Add '34.4' to each side of the equation. -34.4 + -8x + 34.4 + x2 = 0 + 34.4 Reorder the terms: -34.4 + 34.4 + -8x + x2 = 0 + 34.4 Combine like terms: -34.4 + 34.4 = 0.0 0.0 + -8x + x2 = 0 + 34.4 -8x + x2 = 0 + 34.4 Combine like terms: 0 + 34.4 = 34.4 -8x + x2 = 34.4 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 = 34.4 + 16 Reorder the terms: 16 + -8x + x2 = 34.4 + 16 Combine like terms: 34.4 + 16 = 50.4 16 + -8x + x2 = 50.4 Factor a perfect square on the left side: (x + -4)(x + -4) = 50.4 Calculate the square root of the right side: 7.09929574 Break this problem into two subproblems by setting (x + -4) equal to 7.09929574 and -7.09929574.Subproblem 1
x + -4 = 7.09929574 Simplifying x + -4 = 7.09929574 Reorder the terms: -4 + x = 7.09929574 Solving -4 + x = 7.09929574 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 = 7.09929574 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.09929574 + 4 x = 7.09929574 + 4 Combine like terms: 7.09929574 + 4 = 11.09929574 x = 11.09929574 Simplifying x = 11.09929574Subproblem 2
x + -4 = -7.09929574 Simplifying x + -4 = -7.09929574 Reorder the terms: -4 + x = -7.09929574 Solving -4 + x = -7.09929574 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 = -7.09929574 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.09929574 + 4 x = -7.09929574 + 4 Combine like terms: -7.09929574 + 4 = -3.09929574 x = -3.09929574 Simplifying x = -3.09929574Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.09929574, -3.09929574}
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