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Simplifying -10x(x + 3) + 5(3x + -5) = 4(x + -5) + 12 Reorder the terms: -10x(3 + x) + 5(3x + -5) = 4(x + -5) + 12 (3 * -10x + x * -10x) + 5(3x + -5) = 4(x + -5) + 12 (-30x + -10x2) + 5(3x + -5) = 4(x + -5) + 12 Reorder the terms: -30x + -10x2 + 5(-5 + 3x) = 4(x + -5) + 12 -30x + -10x2 + (-5 * 5 + 3x * 5) = 4(x + -5) + 12 -30x + -10x2 + (-25 + 15x) = 4(x + -5) + 12 Reorder the terms: -25 + -30x + 15x + -10x2 = 4(x + -5) + 12 Combine like terms: -30x + 15x = -15x -25 + -15x + -10x2 = 4(x + -5) + 12 Reorder the terms: -25 + -15x + -10x2 = 4(-5 + x) + 12 -25 + -15x + -10x2 = (-5 * 4 + x * 4) + 12 -25 + -15x + -10x2 = (-20 + 4x) + 12 Reorder the terms: -25 + -15x + -10x2 = -20 + 12 + 4x Combine like terms: -20 + 12 = -8 -25 + -15x + -10x2 = -8 + 4x Solving -25 + -15x + -10x2 = -8 + 4x Solving for variable 'x'. Reorder the terms: -25 + 8 + -15x + -4x + -10x2 = -8 + 4x + 8 + -4x Combine like terms: -25 + 8 = -17 -17 + -15x + -4x + -10x2 = -8 + 4x + 8 + -4x Combine like terms: -15x + -4x = -19x -17 + -19x + -10x2 = -8 + 4x + 8 + -4x Reorder the terms: -17 + -19x + -10x2 = -8 + 8 + 4x + -4x Combine like terms: -8 + 8 = 0 -17 + -19x + -10x2 = 0 + 4x + -4x -17 + -19x + -10x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -17 + -19x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 19x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 19x + 10x2)' equal to zero and attempt to solve: Simplifying 17 + 19x + 10x2 = 0 Solving 17 + 19x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.7 + 1.9x + x2 = 0.0 Move the constant term to the right: Add '-1.7' to each side of the equation. 1.7 + 1.9x + -1.7 + x2 = 0.0 + -1.7 Reorder the terms: 1.7 + -1.7 + 1.9x + x2 = 0.0 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + 1.9x + x2 = 0.0 + -1.7 1.9x + x2 = 0.0 + -1.7 Combine like terms: 0.0 + -1.7 = -1.7 1.9x + x2 = -1.7 The x term is 1.9x. Take half its coefficient (0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. 1.9x + 0.9025 + x2 = -1.7 + 0.9025 Reorder the terms: 0.9025 + 1.9x + x2 = -1.7 + 0.9025 Combine like terms: -1.7 + 0.9025 = -0.7975 0.9025 + 1.9x + x2 = -0.7975 Factor a perfect square on the left side: (x + 0.95)(x + 0.95) = -0.7975 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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