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Simplifying 7(x + -4) * 2 + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms: 7(-4 + x) * 2 + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms for easier multiplication: 7 * 2(-4 + x) + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 Multiply 7 * 2 14(-4 + x) + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 (-4 * 14 + x * 14) + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 (-56 + 14x) + -3(x + 5) * 2 + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms: -56 + 14x + -3(5 + x) * 2 + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms for easier multiplication: -56 + 14x + -3 * 2(5 + x) + -4(x + 1)(x + -2) + -2 = 0 Multiply -3 * 2 -56 + 14x + -6(5 + x) + -4(x + 1)(x + -2) + -2 = 0 -56 + 14x + (5 * -6 + x * -6) + -4(x + 1)(x + -2) + -2 = 0 -56 + 14x + (-30 + -6x) + -4(x + 1)(x + -2) + -2 = 0 Reorder the terms: -56 + 14x + -30 + -6x + -4(1 + x)(x + -2) + -2 = 0 Reorder the terms: -56 + 14x + -30 + -6x + -4(1 + x)(-2 + x) + -2 = 0 Multiply (1 + x) * (-2 + x) -56 + 14x + -30 + -6x + -4(1(-2 + x) + x(-2 + x)) + -2 = 0 -56 + 14x + -30 + -6x + -4((-2 * 1 + x * 1) + x(-2 + x)) + -2 = 0 -56 + 14x + -30 + -6x + -4((-2 + 1x) + x(-2 + x)) + -2 = 0 -56 + 14x + -30 + -6x + -4(-2 + 1x + (-2 * x + x * x)) + -2 = 0 -56 + 14x + -30 + -6x + -4(-2 + 1x + (-2x + x2)) + -2 = 0 Combine like terms: 1x + -2x = -1x -56 + 14x + -30 + -6x + -4(-2 + -1x + x2) + -2 = 0 -56 + 14x + -30 + -6x + (-2 * -4 + -1x * -4 + x2 * -4) + -2 = 0 -56 + 14x + -30 + -6x + (8 + 4x + -4x2) + -2 = 0 Reorder the terms: -56 + -30 + 8 + -2 + 14x + -6x + 4x + -4x2 = 0 Combine like terms: -56 + -30 = -86 -86 + 8 + -2 + 14x + -6x + 4x + -4x2 = 0 Combine like terms: -86 + 8 = -78 -78 + -2 + 14x + -6x + 4x + -4x2 = 0 Combine like terms: -78 + -2 = -80 -80 + 14x + -6x + 4x + -4x2 = 0 Combine like terms: 14x + -6x = 8x -80 + 8x + 4x + -4x2 = 0 Combine like terms: 8x + 4x = 12x -80 + 12x + -4x2 = 0 Solving -80 + 12x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-20 + 3x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-20 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -20 + 3x + -1x2 = 0 Solving -20 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -3x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -3x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -3x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -3x + x2 = 0 + -20 -3x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -3x + x2 = -20 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 = -20 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -20 + 2.25 Combine like terms: -20 + 2.25 = -17.75 2.25 + -3x + x2 = -17.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -17.75 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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