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Simplifying (-7x + 5) + -1(x2 + x + -9) = 0 Reorder the terms: (5 + -7x) + -1(x2 + x + -9) = 0 Remove parenthesis around (5 + -7x) 5 + -7x + -1(x2 + x + -9) = 0 Reorder the terms: 5 + -7x + -1(-9 + x + x2) = 0 5 + -7x + (-9 * -1 + x * -1 + x2 * -1) = 0 5 + -7x + (9 + -1x + -1x2) = 0 Reorder the terms: 5 + 9 + -7x + -1x + -1x2 = 0 Combine like terms: 5 + 9 = 14 14 + -7x + -1x + -1x2 = 0 Combine like terms: -7x + -1x = -8x 14 + -8x + -1x2 = 0 Solving 14 + -8x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 8x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 8x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 8x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 8x + x2 = 0 + 14 8x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 8x + x2 = 14 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 = 14 + 16 Reorder the terms: 16 + 8x + x2 = 14 + 16 Combine like terms: 14 + 16 = 30 16 + 8x + x2 = 30 Factor a perfect square on the left side: (x + 4)(x + 4) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 4) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 4 = 5.477225575 Simplifying x + 4 = 5.477225575 Reorder the terms: 4 + x = 5.477225575 Solving 4 + x = 5.477225575 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 = 5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.477225575 + -4 x = 5.477225575 + -4 Combine like terms: 5.477225575 + -4 = 1.477225575 x = 1.477225575 Simplifying x = 1.477225575Subproblem 2
x + 4 = -5.477225575 Simplifying x + 4 = -5.477225575 Reorder the terms: 4 + x = -5.477225575 Solving 4 + x = -5.477225575 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 = -5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.477225575 + -4 x = -5.477225575 + -4 Combine like terms: -5.477225575 + -4 = -9.477225575 x = -9.477225575 Simplifying x = -9.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.477225575, -9.477225575}
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