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Simplifying 86 = 16x2 + -23x Reorder the terms: 86 = -23x + 16x2 Solving 86 = -23x + 16x2 Solving for variable 'x'. Reorder the terms: 86 + 23x + -16x2 = -23x + 23x + 16x2 + -16x2 Combine like terms: -23x + 23x = 0 86 + 23x + -16x2 = 0 + 16x2 + -16x2 86 + 23x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 86 + 23x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -5.375 + -1.4375x + x2 = 0 Move the constant term to the right: Add '5.375' to each side of the equation. -5.375 + -1.4375x + 5.375 + x2 = 0 + 5.375 Reorder the terms: -5.375 + 5.375 + -1.4375x + x2 = 0 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + -1.4375x + x2 = 0 + 5.375 -1.4375x + x2 = 0 + 5.375 Combine like terms: 0 + 5.375 = 5.375 -1.4375x + x2 = 5.375 The x term is -1.4375x. Take half its coefficient (-0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. -1.4375x + 0.5166015625 + x2 = 5.375 + 0.5166015625 Reorder the terms: 0.5166015625 + -1.4375x + x2 = 5.375 + 0.5166015625 Combine like terms: 5.375 + 0.5166015625 = 5.8916015625 0.5166015625 + -1.4375x + x2 = 5.8916015625 Factor a perfect square on the left side: (x + -0.71875)(x + -0.71875) = 5.8916015625 Calculate the square root of the right side: 2.427262154 Break this problem into two subproblems by setting (x + -0.71875) equal to 2.427262154 and -2.427262154.Subproblem 1
x + -0.71875 = 2.427262154 Simplifying x + -0.71875 = 2.427262154 Reorder the terms: -0.71875 + x = 2.427262154 Solving -0.71875 + x = 2.427262154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.71875' to each side of the equation. -0.71875 + 0.71875 + x = 2.427262154 + 0.71875 Combine like terms: -0.71875 + 0.71875 = 0.00000 0.00000 + x = 2.427262154 + 0.71875 x = 2.427262154 + 0.71875 Combine like terms: 2.427262154 + 0.71875 = 3.146012154 x = 3.146012154 Simplifying x = 3.146012154Subproblem 2
x + -0.71875 = -2.427262154 Simplifying x + -0.71875 = -2.427262154 Reorder the terms: -0.71875 + x = -2.427262154 Solving -0.71875 + x = -2.427262154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.71875' to each side of the equation. -0.71875 + 0.71875 + x = -2.427262154 + 0.71875 Combine like terms: -0.71875 + 0.71875 = 0.00000 0.00000 + x = -2.427262154 + 0.71875 x = -2.427262154 + 0.71875 Combine like terms: -2.427262154 + 0.71875 = -1.708512154 x = -1.708512154 Simplifying x = -1.708512154Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.146012154, -1.708512154}
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