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Simplifying (8x2 + -6x + -7) + -1(5 + -9x2 + x) = 0 Reorder the terms: (-7 + -6x + 8x2) + -1(5 + -9x2 + x) = 0 Remove parenthesis around (-7 + -6x + 8x2) -7 + -6x + 8x2 + -1(5 + -9x2 + x) = 0 Reorder the terms: -7 + -6x + 8x2 + -1(5 + x + -9x2) = 0 -7 + -6x + 8x2 + (5 * -1 + x * -1 + -9x2 * -1) = 0 -7 + -6x + 8x2 + (-5 + -1x + 9x2) = 0 Reorder the terms: -7 + -5 + -6x + -1x + 8x2 + 9x2 = 0 Combine like terms: -7 + -5 = -12 -12 + -6x + -1x + 8x2 + 9x2 = 0 Combine like terms: -6x + -1x = -7x -12 + -7x + 8x2 + 9x2 = 0 Combine like terms: 8x2 + 9x2 = 17x2 -12 + -7x + 17x2 = 0 Solving -12 + -7x + 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'. -0.7058823529 + -0.4117647059x + x2 = 0 Move the constant term to the right: Add '0.7058823529' to each side of the equation. -0.7058823529 + -0.4117647059x + 0.7058823529 + x2 = 0 + 0.7058823529 Reorder the terms: -0.7058823529 + 0.7058823529 + -0.4117647059x + x2 = 0 + 0.7058823529 Combine like terms: -0.7058823529 + 0.7058823529 = 0.0000000000 0.0000000000 + -0.4117647059x + x2 = 0 + 0.7058823529 -0.4117647059x + x2 = 0 + 0.7058823529 Combine like terms: 0 + 0.7058823529 = 0.7058823529 -0.4117647059x + x2 = 0.7058823529 The x term is -0.4117647059x. Take half its coefficient (-0.205882353). Square it (0.04238754328) and add it to both sides. Add '0.04238754328' to each side of the equation. -0.4117647059x + 0.04238754328 + x2 = 0.7058823529 + 0.04238754328 Reorder the terms: 0.04238754328 + -0.4117647059x + x2 = 0.7058823529 + 0.04238754328 Combine like terms: 0.7058823529 + 0.04238754328 = 0.74826989618 0.04238754328 + -0.4117647059x + x2 = 0.74826989618 Factor a perfect square on the left side: (x + -0.205882353)(x + -0.205882353) = 0.74826989618 Calculate the square root of the right side: 0.865025951 Break this problem into two subproblems by setting (x + -0.205882353) equal to 0.865025951 and -0.865025951.Subproblem 1
x + -0.205882353 = 0.865025951 Simplifying x + -0.205882353 = 0.865025951 Reorder the terms: -0.205882353 + x = 0.865025951 Solving -0.205882353 + x = 0.865025951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.205882353' to each side of the equation. -0.205882353 + 0.205882353 + x = 0.865025951 + 0.205882353 Combine like terms: -0.205882353 + 0.205882353 = 0.000000000 0.000000000 + x = 0.865025951 + 0.205882353 x = 0.865025951 + 0.205882353 Combine like terms: 0.865025951 + 0.205882353 = 1.070908304 x = 1.070908304 Simplifying x = 1.070908304Subproblem 2
x + -0.205882353 = -0.865025951 Simplifying x + -0.205882353 = -0.865025951 Reorder the terms: -0.205882353 + x = -0.865025951 Solving -0.205882353 + x = -0.865025951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.205882353' to each side of the equation. -0.205882353 + 0.205882353 + x = -0.865025951 + 0.205882353 Combine like terms: -0.205882353 + 0.205882353 = 0.000000000 0.000000000 + x = -0.865025951 + 0.205882353 x = -0.865025951 + 0.205882353 Combine like terms: -0.865025951 + 0.205882353 = -0.659143598 x = -0.659143598 Simplifying x = -0.659143598Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.070908304, -0.659143598}
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