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Simplifying -1x2 + 8x + 75 = 13 Reorder the terms: 75 + 8x + -1x2 = 13 Solving 75 + 8x + -1x2 = 13 Solving for variable 'x'. Reorder the terms: 75 + -13 + 8x + -1x2 = 13 + -13 Combine like terms: 75 + -13 = 62 62 + 8x + -1x2 = 13 + -13 Combine like terms: 13 + -13 = 0 62 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -62 + -8x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + -8x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -8x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -8x + x2 = 0 + 62 -8x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -8x + x2 = 62 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 62 + 16 Reorder the terms: 16 + -8x + x2 = 62 + 16 Combine like terms: 62 + 16 = 78 16 + -8x + x2 = 78 Factor a perfect square on the left side: (x + -4)(x + -4) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + -4) equal to 8.831760866 and -8.831760866.Subproblem 1
x + -4 = 8.831760866 Simplifying x + -4 = 8.831760866 Reorder the terms: -4 + x = 8.831760866 Solving -4 + x = 8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.831760866 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.831760866 + 4 x = 8.831760866 + 4 Combine like terms: 8.831760866 + 4 = 12.831760866 x = 12.831760866 Simplifying x = 12.831760866Subproblem 2
x + -4 = -8.831760866 Simplifying x + -4 = -8.831760866 Reorder the terms: -4 + x = -8.831760866 Solving -4 + x = -8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.831760866 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.831760866 + 4 x = -8.831760866 + 4 Combine like terms: -8.831760866 + 4 = -4.831760866 x = -4.831760866 Simplifying x = -4.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.831760866, -4.831760866}
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