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Simplifying (-9 + -1x)(7 + -1x) = x Multiply (-9 + -1x) * (7 + -1x) (-9(7 + -1x) + -1x * (7 + -1x)) = x ((7 * -9 + -1x * -9) + -1x * (7 + -1x)) = x ((-63 + 9x) + -1x * (7 + -1x)) = x (-63 + 9x + (7 * -1x + -1x * -1x)) = x (-63 + 9x + (-7x + 1x2)) = x Combine like terms: 9x + -7x = 2x (-63 + 2x + 1x2) = x Solving -63 + 2x + 1x2 = x Solving for variable 'x'. Reorder the terms: -63 + 2x + -1x + 1x2 = x + -1x Combine like terms: 2x + -1x = 1x -63 + 1x + 1x2 = x + -1x Combine like terms: x + -1x = 0 -63 + 1x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 1x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 1x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 1x + x2 = 0 + 63 1x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 1x + x2 = 63 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 63 + 0.25 Reorder the terms: 0.25 + x + x2 = 63 + 0.25 Combine like terms: 63 + 0.25 = 63.25 0.25 + x + x2 = 63.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + 0.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x + 0.5 = 7.95298686 Simplifying x + 0.5 = 7.95298686 Reorder the terms: 0.5 + x = 7.95298686 Solving 0.5 + x = 7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.95298686 + -0.5 x = 7.95298686 + -0.5 Combine like terms: 7.95298686 + -0.5 = 7.45298686 x = 7.45298686 Simplifying x = 7.45298686Subproblem 2
x + 0.5 = -7.95298686 Simplifying x + 0.5 = -7.95298686 Reorder the terms: 0.5 + x = -7.95298686 Solving 0.5 + x = -7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.95298686 + -0.5 x = -7.95298686 + -0.5 Combine like terms: -7.95298686 + -0.5 = -8.45298686 x = -8.45298686 Simplifying x = -8.45298686Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.45298686, -8.45298686}
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