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Simplifying 6x2 = 2x2 + -16x + 39 Reorder the terms: 6x2 = 39 + -16x + 2x2 Solving 6x2 = 39 + -16x + 2x2 Solving for variable 'x'. Reorder the terms: -39 + 16x + 6x2 + -2x2 = 39 + -16x + 2x2 + -39 + 16x + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 -39 + 16x + 4x2 = 39 + -16x + 2x2 + -39 + 16x + -2x2 Reorder the terms: -39 + 16x + 4x2 = 39 + -39 + -16x + 16x + 2x2 + -2x2 Combine like terms: 39 + -39 = 0 -39 + 16x + 4x2 = 0 + -16x + 16x + 2x2 + -2x2 -39 + 16x + 4x2 = -16x + 16x + 2x2 + -2x2 Combine like terms: -16x + 16x = 0 -39 + 16x + 4x2 = 0 + 2x2 + -2x2 -39 + 16x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -39 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.75 + 4x + x2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + 4x + 9.75 + x2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + 4x + x2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + 4x + x2 = 0 + 9.75 4x + x2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 4x + x2 = 9.75 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 9.75 + 4 Reorder the terms: 4 + 4x + x2 = 9.75 + 4 Combine like terms: 9.75 + 4 = 13.75 4 + 4x + x2 = 13.75 Factor a perfect square on the left side: (x + 2)(x + 2) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x + 2) equal to 3.708099244 and -3.708099244.Subproblem 1
x + 2 = 3.708099244 Simplifying x + 2 = 3.708099244 Reorder the terms: 2 + x = 3.708099244 Solving 2 + x = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.708099244 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.708099244 + -2 x = 3.708099244 + -2 Combine like terms: 3.708099244 + -2 = 1.708099244 x = 1.708099244 Simplifying x = 1.708099244Subproblem 2
x + 2 = -3.708099244 Simplifying x + 2 = -3.708099244 Reorder the terms: 2 + x = -3.708099244 Solving 2 + x = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.708099244 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.708099244 + -2 x = -3.708099244 + -2 Combine like terms: -3.708099244 + -2 = -5.708099244 x = -5.708099244 Simplifying x = -5.708099244Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.708099244, -5.708099244}
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