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Simplifying (x + -3)(x + 2) = 63 Reorder the terms: (-3 + x)(x + 2) = 63 Reorder the terms: (-3 + x)(2 + x) = 63 Multiply (-3 + x) * (2 + x) (-3(2 + x) + x(2 + x)) = 63 ((2 * -3 + x * -3) + x(2 + x)) = 63 ((-6 + -3x) + x(2 + x)) = 63 (-6 + -3x + (2 * x + x * x)) = 63 (-6 + -3x + (2x + x2)) = 63 Combine like terms: -3x + 2x = -1x (-6 + -1x + x2) = 63 Solving -6 + -1x + x2 = 63 Solving for variable 'x'. Reorder the terms: -6 + -63 + -1x + x2 = 63 + -63 Combine like terms: -6 + -63 = -69 -69 + -1x + x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -69 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + -1x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + -1x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + -1x + x2 = 0 + 69 -1x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 -1x + x2 = 69 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. -1x + 0.25 + x2 = 69 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 69 + 0.25 Combine like terms: 69 + 0.25 = 69.25 0.25 + -1x + x2 = 69.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + -0.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + -0.5 = 8.321658489 Simplifying x + -0.5 = 8.321658489 Reorder the terms: -0.5 + x = 8.321658489 Solving -0.5 + x = 8.321658489 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 = 8.321658489 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.321658489 + 0.5 x = 8.321658489 + 0.5 Combine like terms: 8.321658489 + 0.5 = 8.821658489 x = 8.821658489 Simplifying x = 8.821658489Subproblem 2
x + -0.5 = -8.321658489 Simplifying x + -0.5 = -8.321658489 Reorder the terms: -0.5 + x = -8.321658489 Solving -0.5 + x = -8.321658489 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 = -8.321658489 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.321658489 + 0.5 x = -8.321658489 + 0.5 Combine like terms: -8.321658489 + 0.5 = -7.821658489 x = -7.821658489 Simplifying x = -7.821658489Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.821658489, -7.821658489}
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