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Simplifying x2 + -1x + 7 = 9x2 + x + -1 Reorder the terms: 7 + -1x + x2 = 9x2 + x + -1 Reorder the terms: 7 + -1x + x2 = -1 + x + 9x2 Solving 7 + -1x + x2 = -1 + x + 9x2 Solving for variable 'x'. Reorder the terms: 7 + 1 + -1x + -1x + x2 + -9x2 = -1 + x + 9x2 + 1 + -1x + -9x2 Combine like terms: 7 + 1 = 8 8 + -1x + -1x + x2 + -9x2 = -1 + x + 9x2 + 1 + -1x + -9x2 Combine like terms: -1x + -1x = -2x 8 + -2x + x2 + -9x2 = -1 + x + 9x2 + 1 + -1x + -9x2 Combine like terms: x2 + -9x2 = -8x2 8 + -2x + -8x2 = -1 + x + 9x2 + 1 + -1x + -9x2 Reorder the terms: 8 + -2x + -8x2 = -1 + 1 + x + -1x + 9x2 + -9x2 Combine like terms: -1 + 1 = 0 8 + -2x + -8x2 = 0 + x + -1x + 9x2 + -9x2 8 + -2x + -8x2 = x + -1x + 9x2 + -9x2 Combine like terms: x + -1x = 0 8 + -2x + -8x2 = 0 + 9x2 + -9x2 8 + -2x + -8x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 8 + -2x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -1x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1x + -4x2)' equal to zero and attempt to solve: Simplifying 4 + -1x + -4x2 = 0 Solving 4 + -1x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1 + 0.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.25x + x2 = 0 + 1 0.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.25x + x2 = 1 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 1 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 1 + 0.015625 Combine like terms: 1 + 0.015625 = 1.015625 0.015625 + 0.25x + x2 = 1.015625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (x + 0.125) equal to 1.007782219 and -1.007782219.Subproblem 1
x + 0.125 = 1.007782219 Simplifying x + 0.125 = 1.007782219 Reorder the terms: 0.125 + x = 1.007782219 Solving 0.125 + x = 1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.007782219 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.007782219 + -0.125 x = 1.007782219 + -0.125 Combine like terms: 1.007782219 + -0.125 = 0.882782219 x = 0.882782219 Simplifying x = 0.882782219Subproblem 2
x + 0.125 = -1.007782219 Simplifying x + 0.125 = -1.007782219 Reorder the terms: 0.125 + x = -1.007782219 Solving 0.125 + x = -1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.007782219 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.007782219 + -0.125 x = -1.007782219 + -0.125 Combine like terms: -1.007782219 + -0.125 = -1.132782219 x = -1.132782219 Simplifying x = -1.132782219Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.882782219, -1.132782219}Solution
x = {0.882782219, -1.132782219}
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