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Simplifying 9x2 + -6x + -59 + 8x2 + 8x = 0 Reorder the terms: -59 + -6x + 8x + 9x2 + 8x2 = 0 Combine like terms: -6x + 8x = 2x -59 + 2x + 9x2 + 8x2 = 0 Combine like terms: 9x2 + 8x2 = 17x2 -59 + 2x + 17x2 = 0 Solving -59 + 2x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -3.470588235 + 0.1176470588x + x2 = 0 Move the constant term to the right: Add '3.470588235' to each side of the equation. -3.470588235 + 0.1176470588x + 3.470588235 + x2 = 0 + 3.470588235 Reorder the terms: -3.470588235 + 3.470588235 + 0.1176470588x + x2 = 0 + 3.470588235 Combine like terms: -3.470588235 + 3.470588235 = 0.000000000 0.000000000 + 0.1176470588x + x2 = 0 + 3.470588235 0.1176470588x + x2 = 0 + 3.470588235 Combine like terms: 0 + 3.470588235 = 3.470588235 0.1176470588x + x2 = 3.470588235 The x term is 0.1176470588x. Take half its coefficient (0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. 0.1176470588x + 0.003460207611 + x2 = 3.470588235 + 0.003460207611 Reorder the terms: 0.003460207611 + 0.1176470588x + x2 = 3.470588235 + 0.003460207611 Combine like terms: 3.470588235 + 0.003460207611 = 3.474048442611 0.003460207611 + 0.1176470588x + x2 = 3.474048442611 Factor a perfect square on the left side: (x + 0.0588235294)(x + 0.0588235294) = 3.474048442611 Calculate the square root of the right side: 1.863879943 Break this problem into two subproblems by setting (x + 0.0588235294) equal to 1.863879943 and -1.863879943.Subproblem 1
x + 0.0588235294 = 1.863879943 Simplifying x + 0.0588235294 = 1.863879943 Reorder the terms: 0.0588235294 + x = 1.863879943 Solving 0.0588235294 + x = 1.863879943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = 1.863879943 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = 1.863879943 + -0.0588235294 x = 1.863879943 + -0.0588235294 Combine like terms: 1.863879943 + -0.0588235294 = 1.8050564136 x = 1.8050564136 Simplifying x = 1.8050564136Subproblem 2
x + 0.0588235294 = -1.863879943 Simplifying x + 0.0588235294 = -1.863879943 Reorder the terms: 0.0588235294 + x = -1.863879943 Solving 0.0588235294 + x = -1.863879943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = -1.863879943 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = -1.863879943 + -0.0588235294 x = -1.863879943 + -0.0588235294 Combine like terms: -1.863879943 + -0.0588235294 = -1.9227034724 x = -1.9227034724 Simplifying x = -1.9227034724Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8050564136, -1.9227034724}
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