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Simplifying x2 + -1(7x + -16) = x + 59 Reorder the terms: x2 + -1(-16 + 7x) = x + 59 x2 + (-16 * -1 + 7x * -1) = x + 59 x2 + (16 + -7x) = x + 59 Reorder the terms: 16 + -7x + x2 = x + 59 Reorder the terms: 16 + -7x + x2 = 59 + x Solving 16 + -7x + x2 = 59 + x Solving for variable 'x'. Reorder the terms: 16 + -59 + -7x + -1x + x2 = 59 + x + -59 + -1x Combine like terms: 16 + -59 = -43 -43 + -7x + -1x + x2 = 59 + x + -59 + -1x Combine like terms: -7x + -1x = -8x -43 + -8x + x2 = 59 + x + -59 + -1x Reorder the terms: -43 + -8x + x2 = 59 + -59 + x + -1x Combine like terms: 59 + -59 = 0 -43 + -8x + x2 = 0 + x + -1x -43 + -8x + x2 = x + -1x Combine like terms: x + -1x = 0 -43 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -8x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -8x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -8x + x2 = 0 + 43 -8x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -8x + x2 = 43 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 = 43 + 16 Reorder the terms: 16 + -8x + x2 = 43 + 16 Combine like terms: 43 + 16 = 59 16 + -8x + x2 = 59 Factor a perfect square on the left side: (x + -4)(x + -4) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + -4) equal to 7.681145748 and -7.681145748.Subproblem 1
x + -4 = 7.681145748 Simplifying x + -4 = 7.681145748 Reorder the terms: -4 + x = 7.681145748 Solving -4 + x = 7.681145748 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 = 7.681145748 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.681145748 + 4 x = 7.681145748 + 4 Combine like terms: 7.681145748 + 4 = 11.681145748 x = 11.681145748 Simplifying x = 11.681145748Subproblem 2
x + -4 = -7.681145748 Simplifying x + -4 = -7.681145748 Reorder the terms: -4 + x = -7.681145748 Solving -4 + x = -7.681145748 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 = -7.681145748 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.681145748 + 4 x = -7.681145748 + 4 Combine like terms: -7.681145748 + 4 = -3.681145748 x = -3.681145748 Simplifying x = -3.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.681145748, -3.681145748}
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