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Simplifying -5x(4x + 6) = 70 Reorder the terms: -5x(6 + 4x) = 70 (6 * -5x + 4x * -5x) = 70 (-30x + -20x2) = 70 Solving -30x + -20x2 = 70 Solving for variable 'x'. Reorder the terms: -70 + -30x + -20x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + -30x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '-10'. -10(7 + 3x + 2x2) = 0 Ignore the factor -10.Subproblem 1
Set the factor '(7 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 7 + 3x + 2x2 = 0 Solving 7 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 1.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 1.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 1.5x + x2 = 0 + -3.5 1.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 1.5x + x2 = -3.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -3.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -3.5 + 0.5625 Combine like terms: -3.5 + 0.5625 = -2.9375 0.5625 + 1.5x + x2 = -2.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -2.9375 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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