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Simplifying 5x(2x + -6) + 9 = 2(2x + -3) + 4x + -23 Reorder the terms: 5x(-6 + 2x) + 9 = 2(2x + -3) + 4x + -23 (-6 * 5x + 2x * 5x) + 9 = 2(2x + -3) + 4x + -23 (-30x + 10x2) + 9 = 2(2x + -3) + 4x + -23 Reorder the terms: 9 + -30x + 10x2 = 2(2x + -3) + 4x + -23 Reorder the terms: 9 + -30x + 10x2 = 2(-3 + 2x) + 4x + -23 9 + -30x + 10x2 = (-3 * 2 + 2x * 2) + 4x + -23 9 + -30x + 10x2 = (-6 + 4x) + 4x + -23 Reorder the terms: 9 + -30x + 10x2 = -6 + -23 + 4x + 4x Combine like terms: -6 + -23 = -29 9 + -30x + 10x2 = -29 + 4x + 4x Combine like terms: 4x + 4x = 8x 9 + -30x + 10x2 = -29 + 8x Solving 9 + -30x + 10x2 = -29 + 8x Solving for variable 'x'. Reorder the terms: 9 + 29 + -30x + -8x + 10x2 = -29 + 8x + 29 + -8x Combine like terms: 9 + 29 = 38 38 + -30x + -8x + 10x2 = -29 + 8x + 29 + -8x Combine like terms: -30x + -8x = -38x 38 + -38x + 10x2 = -29 + 8x + 29 + -8x Reorder the terms: 38 + -38x + 10x2 = -29 + 29 + 8x + -8x Combine like terms: -29 + 29 = 0 38 + -38x + 10x2 = 0 + 8x + -8x 38 + -38x + 10x2 = 8x + -8x Combine like terms: 8x + -8x = 0 38 + -38x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -19x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -19x + 5x2)' equal to zero and attempt to solve: Simplifying 19 + -19x + 5x2 = 0 Solving 19 + -19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.8 + -3.8x + x2 = 0 Move the constant term to the right: Add '-3.8' to each side of the equation. 3.8 + -3.8x + -3.8 + x2 = 0 + -3.8 Reorder the terms: 3.8 + -3.8 + -3.8x + x2 = 0 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + -3.8x + x2 = 0 + -3.8 -3.8x + x2 = 0 + -3.8 Combine like terms: 0 + -3.8 = -3.8 -3.8x + x2 = -3.8 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = -3.8 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = -3.8 + 3.61 Combine like terms: -3.8 + 3.61 = -0.19 3.61 + -3.8x + x2 = -0.19 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = -0.19 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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