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Simplifying (x + 5)(x) = 2(x + 5)(x + -2) + 70 Reorder the terms: (5 + x)(x) = 2(x + 5)(x + -2) + 70 Reorder the terms for easier multiplication: x(5 + x) = 2(x + 5)(x + -2) + 70 (5 * x + x * x) = 2(x + 5)(x + -2) + 70 (5x + x2) = 2(x + 5)(x + -2) + 70 Reorder the terms: 5x + x2 = 2(5 + x)(x + -2) + 70 Reorder the terms: 5x + x2 = 2(5 + x)(-2 + x) + 70 Multiply (5 + x) * (-2 + x) 5x + x2 = 2(5(-2 + x) + x(-2 + x)) + 70 5x + x2 = 2((-2 * 5 + x * 5) + x(-2 + x)) + 70 5x + x2 = 2((-10 + 5x) + x(-2 + x)) + 70 5x + x2 = 2(-10 + 5x + (-2 * x + x * x)) + 70 5x + x2 = 2(-10 + 5x + (-2x + x2)) + 70 Combine like terms: 5x + -2x = 3x 5x + x2 = 2(-10 + 3x + x2) + 70 5x + x2 = (-10 * 2 + 3x * 2 + x2 * 2) + 70 5x + x2 = (-20 + 6x + 2x2) + 70 Reorder the terms: 5x + x2 = -20 + 70 + 6x + 2x2 Combine like terms: -20 + 70 = 50 5x + x2 = 50 + 6x + 2x2 Solving 5x + x2 = 50 + 6x + 2x2 Solving for variable 'x'. Reorder the terms: -50 + 5x + -6x + x2 + -2x2 = 50 + 6x + 2x2 + -50 + -6x + -2x2 Combine like terms: 5x + -6x = -1x -50 + -1x + x2 + -2x2 = 50 + 6x + 2x2 + -50 + -6x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -50 + -1x + -1x2 = 50 + 6x + 2x2 + -50 + -6x + -2x2 Reorder the terms: -50 + -1x + -1x2 = 50 + -50 + 6x + -6x + 2x2 + -2x2 Combine like terms: 50 + -50 = 0 -50 + -1x + -1x2 = 0 + 6x + -6x + 2x2 + -2x2 -50 + -1x + -1x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 -50 + -1x + -1x2 = 0 + 2x2 + -2x2 -50 + -1x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -50 + -1x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(50 + x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(50 + x + x2)' equal to zero and attempt to solve: Simplifying 50 + x + x2 = 0 Solving 50 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + x + x2 = 0 + -50 x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 x + x2 = -50 The x term is x. 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 = -50 + 0.25 Reorder the terms: 0.25 + x + x2 = -50 + 0.25 Combine like terms: -50 + 0.25 = -49.75 0.25 + x + x2 = -49.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -49.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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