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Simplifying 8x6 + 63x3 + 8 = 0 Reorder the terms: 8 + 63x3 + 8x6 = 0 Solving 8 + 63x3 + 8x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1 + 7.875x3 + x6 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 7.875x3 + -1 + x6 = 0 + -1 Reorder the terms: 1 + -1 + 7.875x3 + x6 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7.875x3 + x6 = 0 + -1 7.875x3 + x6 = 0 + -1 Combine like terms: 0 + -1 = -1 7.875x3 + x6 = -1 The x term is 7.875x3. Take half its coefficient (3.9375). Square it (15.50390625) and add it to both sides. Add '15.50390625' to each side of the equation. 7.875x3 + 15.50390625 + x6 = -1 + 15.50390625 Reorder the terms: 15.50390625 + 7.875x3 + x6 = -1 + 15.50390625 Combine like terms: -1 + 15.50390625 = 14.50390625 15.50390625 + 7.875x3 + x6 = 14.50390625 Factor a perfect square on the left side: (x3 + 3.9375)(x3 + 3.9375) = 14.50390625 Calculate the square root of the right side: 3.808399434 Break this problem into two subproblems by setting (x3 + 3.9375) equal to 3.808399434 and -3.808399434.Subproblem 1
x3 + 3.9375 = 3.808399434 Simplifying x3 + 3.9375 = 3.808399434 Reorder the terms: 3.9375 + x3 = 3.808399434 Solving 3.9375 + x3 = 3.808399434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9375' to each side of the equation. 3.9375 + -3.9375 + x3 = 3.808399434 + -3.9375 Combine like terms: 3.9375 + -3.9375 = 0.0000 0.0000 + x3 = 3.808399434 + -3.9375 x3 = 3.808399434 + -3.9375 Combine like terms: 3.808399434 + -3.9375 = -0.129100566 x3 = -0.129100566 Simplifying x3 = -0.129100566 Reorder the terms: 0.129100566 + x3 = -0.129100566 + 0.129100566 Combine like terms: -0.129100566 + 0.129100566 = 0.000000000 0.129100566 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + 3.9375 = -3.808399434 Simplifying x3 + 3.9375 = -3.808399434 Reorder the terms: 3.9375 + x3 = -3.808399434 Solving 3.9375 + x3 = -3.808399434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9375' to each side of the equation. 3.9375 + -3.9375 + x3 = -3.808399434 + -3.9375 Combine like terms: 3.9375 + -3.9375 = 0.0000 0.0000 + x3 = -3.808399434 + -3.9375 x3 = -3.808399434 + -3.9375 Combine like terms: -3.808399434 + -3.9375 = -7.745899434 x3 = -7.745899434 Simplifying x3 = -7.745899434 Reorder the terms: 7.745899434 + x3 = -7.745899434 + 7.745899434 Combine like terms: -7.745899434 + 7.745899434 = 0.000000000 7.745899434 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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