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Simplifying 7(x + -4) * 2 + -3(x + 5) * 2 = 4(x + 1)(x + -1) + -2 Reorder the terms: 7(-4 + x) * 2 + -3(x + 5) * 2 = 4(x + 1)(x + -1) + -2 Reorder the terms for easier multiplication: 7 * 2(-4 + x) + -3(x + 5) * 2 = 4(x + 1)(x + -1) + -2 Multiply 7 * 2 14(-4 + x) + -3(x + 5) * 2 = 4(x + 1)(x + -1) + -2 (-4 * 14 + x * 14) + -3(x + 5) * 2 = 4(x + 1)(x + -1) + -2 (-56 + 14x) + -3(x + 5) * 2 = 4(x + 1)(x + -1) + -2 Reorder the terms: -56 + 14x + -3(5 + x) * 2 = 4(x + 1)(x + -1) + -2 Reorder the terms for easier multiplication: -56 + 14x + -3 * 2(5 + x) = 4(x + 1)(x + -1) + -2 Multiply -3 * 2 -56 + 14x + -6(5 + x) = 4(x + 1)(x + -1) + -2 -56 + 14x + (5 * -6 + x * -6) = 4(x + 1)(x + -1) + -2 -56 + 14x + (-30 + -6x) = 4(x + 1)(x + -1) + -2 Reorder the terms: -56 + -30 + 14x + -6x = 4(x + 1)(x + -1) + -2 Combine like terms: -56 + -30 = -86 -86 + 14x + -6x = 4(x + 1)(x + -1) + -2 Combine like terms: 14x + -6x = 8x -86 + 8x = 4(x + 1)(x + -1) + -2 Reorder the terms: -86 + 8x = 4(1 + x)(x + -1) + -2 Reorder the terms: -86 + 8x = 4(1 + x)(-1 + x) + -2 Multiply (1 + x) * (-1 + x) -86 + 8x = 4(1(-1 + x) + x(-1 + x)) + -2 -86 + 8x = 4((-1 * 1 + x * 1) + x(-1 + x)) + -2 -86 + 8x = 4((-1 + 1x) + x(-1 + x)) + -2 -86 + 8x = 4(-1 + 1x + (-1 * x + x * x)) + -2 -86 + 8x = 4(-1 + 1x + (-1x + x2)) + -2 Combine like terms: 1x + -1x = 0 -86 + 8x = 4(-1 + 0 + x2) + -2 -86 + 8x = 4(-1 + x2) + -2 -86 + 8x = (-1 * 4 + x2 * 4) + -2 -86 + 8x = (-4 + 4x2) + -2 Reorder the terms: -86 + 8x = -4 + -2 + 4x2 Combine like terms: -4 + -2 = -6 -86 + 8x = -6 + 4x2 Solving -86 + 8x = -6 + 4x2 Solving for variable 'x'. Reorder the terms: -86 + 6 + 8x + -4x2 = -6 + 4x2 + 6 + -4x2 Combine like terms: -86 + 6 = -80 -80 + 8x + -4x2 = -6 + 4x2 + 6 + -4x2 Reorder the terms: -80 + 8x + -4x2 = -6 + 6 + 4x2 + -4x2 Combine like terms: -6 + 6 = 0 -80 + 8x + -4x2 = 0 + 4x2 + -4x2 -80 + 8x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -80 + 8x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-20 + 2x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-20 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -20 + 2x + -1x2 = 0 Solving -20 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -2x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -2x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -2x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -2x + x2 = 0 + -20 -2x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -2x + x2 = -20 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -20 + 1 Reorder the terms: 1 + -2x + x2 = -20 + 1 Combine like terms: -20 + 1 = -19 1 + -2x + x2 = -19 Factor a perfect square on the left side: (x + -1)(x + -1) = -19 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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