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Simplifying -9x8 + -6x4 + 17 = 0 Reorder the terms: 17 + -6x4 + -9x8 = 0 Solving 17 + -6x4 + -9x8 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.888888889 + 0.6666666667x4 + x8 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + 0.6666666667x4 + 1.888888889 + x8 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + 0.6666666667x4 + x8 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + 0.6666666667x4 + x8 = 0 + 1.888888889 0.6666666667x4 + x8 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 0.6666666667x4 + x8 = 1.888888889 The x term is 0.6666666667x4. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x4 + 0.1111111112 + x8 = 1.888888889 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x4 + x8 = 1.888888889 + 0.1111111112 Combine like terms: 1.888888889 + 0.1111111112 = 2.0000000002 0.1111111112 + 0.6666666667x4 + x8 = 2.0000000002 Factor a perfect square on the left side: (x4 + 0.3333333334)(x4 + 0.3333333334) = 2.0000000002 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x4 + 0.3333333334) equal to 1.414213562 and -1.414213562.Subproblem 1
x4 + 0.3333333334 = 1.414213562 Simplifying x4 + 0.3333333334 = 1.414213562 Reorder the terms: 0.3333333334 + x4 = 1.414213562 Solving 0.3333333334 + x4 = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x4 = 1.414213562 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x4 = 1.414213562 + -0.3333333334 x4 = 1.414213562 + -0.3333333334 Combine like terms: 1.414213562 + -0.3333333334 = 1.0808802286 x4 = 1.0808802286 Simplifying x4 = 1.0808802286 Reorder the terms: -1.0808802286 + x4 = 1.0808802286 + -1.0808802286 Combine like terms: 1.0808802286 + -1.0808802286 = 0.0000000000 -1.0808802286 + x4 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x4 + 0.3333333334 = -1.414213562 Simplifying x4 + 0.3333333334 = -1.414213562 Reorder the terms: 0.3333333334 + x4 = -1.414213562 Solving 0.3333333334 + x4 = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x4 = -1.414213562 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x4 = -1.414213562 + -0.3333333334 x4 = -1.414213562 + -0.3333333334 Combine like terms: -1.414213562 + -0.3333333334 = -1.7475468954 x4 = -1.7475468954 Simplifying x4 = -1.7475468954 Reorder the terms: 1.7475468954 + x4 = -1.7475468954 + 1.7475468954 Combine like terms: -1.7475468954 + 1.7475468954 = 0.0000000000 1.7475468954 + x4 = 0.0000000000 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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