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Simplifying x + x(x + -9) = 43 Reorder the terms: x + x(-9 + x) = 43 x + (-9 * x + x * x) = 43 x + (-9x + x2) = 43 Combine like terms: x + -9x = -8x -8x + x2 = 43 Solving -8x + x2 = 43 Solving for variable 'x'. Reorder the terms: -43 + -8x + x2 = 43 + -43 Combine like terms: 43 + -43 = 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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