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Simplifying 2x(x + -1) + 15 = 90 Reorder the terms: 2x(-1 + x) + 15 = 90 (-1 * 2x + x * 2x) + 15 = 90 (-2x + 2x2) + 15 = 90 Reorder the terms: 15 + -2x + 2x2 = 90 Solving 15 + -2x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: 15 + -90 + -2x + 2x2 = 90 + -90 Combine like terms: 15 + -90 = -75 -75 + -2x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -75 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -37.5 + -1x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + -1x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + -1x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + -1x + x2 = 0 + 37.5 -1x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 -1x + x2 = 37.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 37.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 37.5 + 0.25 Combine like terms: 37.5 + 0.25 = 37.75 0.25 + -1x + x2 = 37.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 37.75 Calculate the square root of the right side: 6.144102864 Break this problem into two subproblems by setting (x + -0.5) equal to 6.144102864 and -6.144102864.Subproblem 1
x + -0.5 = 6.144102864 Simplifying x + -0.5 = 6.144102864 Reorder the terms: -0.5 + x = 6.144102864 Solving -0.5 + x = 6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 6.144102864 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.144102864 + 0.5 x = 6.144102864 + 0.5 Combine like terms: 6.144102864 + 0.5 = 6.644102864 x = 6.644102864 Simplifying x = 6.644102864Subproblem 2
x + -0.5 = -6.144102864 Simplifying x + -0.5 = -6.144102864 Reorder the terms: -0.5 + x = -6.144102864 Solving -0.5 + x = -6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -6.144102864 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.144102864 + 0.5 x = -6.144102864 + 0.5 Combine like terms: -6.144102864 + 0.5 = -5.644102864 x = -5.644102864 Simplifying x = -5.644102864Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.644102864, -5.644102864}
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