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Simplifying 16x2 + -24x = 87 Reorder the terms: -24x + 16x2 = 87 Solving -24x + 16x2 = 87 Solving for variable 'x'. Reorder the terms: -87 + -24x + 16x2 = 87 + -87 Combine like terms: 87 + -87 = 0 -87 + -24x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.4375 + -1.5x + x2 = 0 Move the constant term to the right: Add '5.4375' to each side of the equation. -5.4375 + -1.5x + 5.4375 + x2 = 0 + 5.4375 Reorder the terms: -5.4375 + 5.4375 + -1.5x + x2 = 0 + 5.4375 Combine like terms: -5.4375 + 5.4375 = 0.0000 0.0000 + -1.5x + x2 = 0 + 5.4375 -1.5x + x2 = 0 + 5.4375 Combine like terms: 0 + 5.4375 = 5.4375 -1.5x + x2 = 5.4375 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 5.4375 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 5.4375 + 0.5625 Combine like terms: 5.4375 + 0.5625 = 6 0.5625 + -1.5x + x2 = 6 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -0.75) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -0.75 = 2.449489743 Simplifying x + -0.75 = 2.449489743 Reorder the terms: -0.75 + x = 2.449489743 Solving -0.75 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.449489743 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.449489743 + 0.75 x = 2.449489743 + 0.75 Combine like terms: 2.449489743 + 0.75 = 3.199489743 x = 3.199489743 Simplifying x = 3.199489743Subproblem 2
x + -0.75 = -2.449489743 Simplifying x + -0.75 = -2.449489743 Reorder the terms: -0.75 + x = -2.449489743 Solving -0.75 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.449489743 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.449489743 + 0.75 x = -2.449489743 + 0.75 Combine like terms: -2.449489743 + 0.75 = -1.699489743 x = -1.699489743 Simplifying x = -1.699489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.199489743, -1.699489743}
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