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Simplifying 5(x + -3) + -2(2x + 3)(5x + 5) = 0 Reorder the terms: 5(-3 + x) + -2(2x + 3)(5x + 5) = 0 (-3 * 5 + x * 5) + -2(2x + 3)(5x + 5) = 0 (-15 + 5x) + -2(2x + 3)(5x + 5) = 0 Reorder the terms: -15 + 5x + -2(3 + 2x)(5x + 5) = 0 Reorder the terms: -15 + 5x + -2(3 + 2x)(5 + 5x) = 0 Multiply (3 + 2x) * (5 + 5x) -15 + 5x + -2(3(5 + 5x) + 2x * (5 + 5x)) = 0 -15 + 5x + -2((5 * 3 + 5x * 3) + 2x * (5 + 5x)) = 0 -15 + 5x + -2((15 + 15x) + 2x * (5 + 5x)) = 0 -15 + 5x + -2(15 + 15x + (5 * 2x + 5x * 2x)) = 0 -15 + 5x + -2(15 + 15x + (10x + 10x2)) = 0 Combine like terms: 15x + 10x = 25x -15 + 5x + -2(15 + 25x + 10x2) = 0 -15 + 5x + (15 * -2 + 25x * -2 + 10x2 * -2) = 0 -15 + 5x + (-30 + -50x + -20x2) = 0 Reorder the terms: -15 + -30 + 5x + -50x + -20x2 = 0 Combine like terms: -15 + -30 = -45 -45 + 5x + -50x + -20x2 = 0 Combine like terms: 5x + -50x = -45x -45 + -45x + -20x2 = 0 Solving -45 + -45x + -20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-5'. -5(9 + 9x + 4x2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(9 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 9x + 4x2 = 0 Solving 9 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 2.25x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 2.25x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 2.25x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 2.25x + x2 = 0 + -2.25 2.25x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 2.25x + x2 = -2.25 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -2.25 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -2.25 + 1.265625 Combine like terms: -2.25 + 1.265625 = -0.984375 1.265625 + 2.25x + x2 = -0.984375 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = -0.984375 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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