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Simplifying 10 = 16x2 + 23x + 6 Reorder the terms: 10 = 6 + 23x + 16x2 Solving 10 = 6 + 23x + 16x2 Solving for variable 'x'. Combine like terms: 10 + -6 = 4 4 + -23x + -16x2 = 6 + 23x + 16x2 + -6 + -23x + -16x2 Reorder the terms: 4 + -23x + -16x2 = 6 + -6 + 23x + -23x + 16x2 + -16x2 Combine like terms: 6 + -6 = 0 4 + -23x + -16x2 = 0 + 23x + -23x + 16x2 + -16x2 4 + -23x + -16x2 = 23x + -23x + 16x2 + -16x2 Combine like terms: 23x + -23x = 0 4 + -23x + -16x2 = 0 + 16x2 + -16x2 4 + -23x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 4 + -23x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.25 + 1.4375x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 1.4375x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 1.4375x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 1.4375x + x2 = 0 + 0.25 1.4375x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 1.4375x + x2 = 0.25 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 = 0.25 + 0.5166015625 Reorder the terms: 0.5166015625 + 1.4375x + x2 = 0.25 + 0.5166015625 Combine like terms: 0.25 + 0.5166015625 = 0.7666015625 0.5166015625 + 1.4375x + x2 = 0.7666015625 Factor a perfect square on the left side: (x + 0.71875)(x + 0.71875) = 0.7666015625 Calculate the square root of the right side: 0.875557858 Break this problem into two subproblems by setting (x + 0.71875) equal to 0.875557858 and -0.875557858.Subproblem 1
x + 0.71875 = 0.875557858 Simplifying x + 0.71875 = 0.875557858 Reorder the terms: 0.71875 + x = 0.875557858 Solving 0.71875 + x = 0.875557858 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 = 0.875557858 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + x = 0.875557858 + -0.71875 x = 0.875557858 + -0.71875 Combine like terms: 0.875557858 + -0.71875 = 0.156807858 x = 0.156807858 Simplifying x = 0.156807858Subproblem 2
x + 0.71875 = -0.875557858 Simplifying x + 0.71875 = -0.875557858 Reorder the terms: 0.71875 + x = -0.875557858 Solving 0.71875 + x = -0.875557858 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 = -0.875557858 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + x = -0.875557858 + -0.71875 x = -0.875557858 + -0.71875 Combine like terms: -0.875557858 + -0.71875 = -1.594307858 x = -1.594307858 Simplifying x = -1.594307858Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.156807858, -1.594307858}
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