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Simplifying 9x + 10 = x(x) + -6x Reorder the terms: 10 + 9x = x(x) + -6x Multiply x * x 10 + 9x = x2 + -6x Reorder the terms: 10 + 9x = -6x + x2 Solving 10 + 9x = -6x + x2 Solving for variable 'x'. Combine like terms: 9x + 6x = 15x 10 + 15x + -1x2 = -6x + x2 + 6x + -1x2 Reorder the terms: 10 + 15x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 10 + 15x + -1x2 = 0 + x2 + -1x2 10 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -15x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -15x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -15x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -15x + x2 = 0 + 10 -15x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -15x + x2 = 10 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 10 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 10 + 56.25 Combine like terms: 10 + 56.25 = 66.25 56.25 + -15x + x2 = 66.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + -7.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + -7.5 = 8.139410298 Simplifying x + -7.5 = 8.139410298 Reorder the terms: -7.5 + x = 8.139410298 Solving -7.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.139410298 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.139410298 + 7.5 x = 8.139410298 + 7.5 Combine like terms: 8.139410298 + 7.5 = 15.639410298 x = 15.639410298 Simplifying x = 15.639410298Subproblem 2
x + -7.5 = -8.139410298 Simplifying x + -7.5 = -8.139410298 Reorder the terms: -7.5 + x = -8.139410298 Solving -7.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.139410298 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.139410298 + 7.5 x = -8.139410298 + 7.5 Combine like terms: -8.139410298 + 7.5 = -0.639410298 x = -0.639410298 Simplifying x = -0.639410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.639410298, -0.639410298}
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