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Simplifying 5(x + 2) + -1(x + -5)(x + -5) = (2x + -3)(2x + 3) + 19 Reorder the terms: 5(2 + x) + -1(x + -5)(x + -5) = (2x + -3)(2x + 3) + 19 (2 * 5 + x * 5) + -1(x + -5)(x + -5) = (2x + -3)(2x + 3) + 19 (10 + 5x) + -1(x + -5)(x + -5) = (2x + -3)(2x + 3) + 19 Reorder the terms: 10 + 5x + -1(-5 + x)(x + -5) = (2x + -3)(2x + 3) + 19 Reorder the terms: 10 + 5x + -1(-5 + x)(-5 + x) = (2x + -3)(2x + 3) + 19 Multiply (-5 + x) * (-5 + x) 10 + 5x + -1(-5(-5 + x) + x(-5 + x)) = (2x + -3)(2x + 3) + 19 10 + 5x + -1((-5 * -5 + x * -5) + x(-5 + x)) = (2x + -3)(2x + 3) + 19 10 + 5x + -1((25 + -5x) + x(-5 + x)) = (2x + -3)(2x + 3) + 19 10 + 5x + -1(25 + -5x + (-5 * x + x * x)) = (2x + -3)(2x + 3) + 19 10 + 5x + -1(25 + -5x + (-5x + x2)) = (2x + -3)(2x + 3) + 19 Combine like terms: -5x + -5x = -10x 10 + 5x + -1(25 + -10x + x2) = (2x + -3)(2x + 3) + 19 10 + 5x + (25 * -1 + -10x * -1 + x2 * -1) = (2x + -3)(2x + 3) + 19 10 + 5x + (-25 + 10x + -1x2) = (2x + -3)(2x + 3) + 19 Reorder the terms: 10 + -25 + 5x + 10x + -1x2 = (2x + -3)(2x + 3) + 19 Combine like terms: 10 + -25 = -15 -15 + 5x + 10x + -1x2 = (2x + -3)(2x + 3) + 19 Combine like terms: 5x + 10x = 15x -15 + 15x + -1x2 = (2x + -3)(2x + 3) + 19 Reorder the terms: -15 + 15x + -1x2 = (-3 + 2x)(2x + 3) + 19 Reorder the terms: -15 + 15x + -1x2 = (-3 + 2x)(3 + 2x) + 19 Multiply (-3 + 2x) * (3 + 2x) -15 + 15x + -1x2 = (-3(3 + 2x) + 2x * (3 + 2x)) + 19 -15 + 15x + -1x2 = ((3 * -3 + 2x * -3) + 2x * (3 + 2x)) + 19 -15 + 15x + -1x2 = ((-9 + -6x) + 2x * (3 + 2x)) + 19 -15 + 15x + -1x2 = (-9 + -6x + (3 * 2x + 2x * 2x)) + 19 -15 + 15x + -1x2 = (-9 + -6x + (6x + 4x2)) + 19 Combine like terms: -6x + 6x = 0 -15 + 15x + -1x2 = (-9 + 0 + 4x2) + 19 -15 + 15x + -1x2 = (-9 + 4x2) + 19 Reorder the terms: -15 + 15x + -1x2 = -9 + 19 + 4x2 Combine like terms: -9 + 19 = 10 -15 + 15x + -1x2 = 10 + 4x2 Solving -15 + 15x + -1x2 = 10 + 4x2 Solving for variable 'x'. Reorder the terms: -15 + -10 + 15x + -1x2 + -4x2 = 10 + 4x2 + -10 + -4x2 Combine like terms: -15 + -10 = -25 -25 + 15x + -1x2 + -4x2 = 10 + 4x2 + -10 + -4x2 Combine like terms: -1x2 + -4x2 = -5x2 -25 + 15x + -5x2 = 10 + 4x2 + -10 + -4x2 Reorder the terms: -25 + 15x + -5x2 = 10 + -10 + 4x2 + -4x2 Combine like terms: 10 + -10 = 0 -25 + 15x + -5x2 = 0 + 4x2 + -4x2 -25 + 15x + -5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -25 + 15x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + 3x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 3x + -1x2 = 0 Solving -5 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -3x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -3x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -3x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x + x2 = 0 + -5 -3x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3x + x2 = -5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -5 + 2.25 Combine like terms: -5 + 2.25 = -2.75 2.25 + -3x + x2 = -2.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -2.75 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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