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Simplifying 7x + -2x(2x + 6) = 5x + 30 Reorder the terms: 7x + -2x(6 + 2x) = 5x + 30 7x + (6 * -2x + 2x * -2x) = 5x + 30 7x + (-12x + -4x2) = 5x + 30 Combine like terms: 7x + -12x = -5x -5x + -4x2 = 5x + 30 Reorder the terms: -5x + -4x2 = 30 + 5x Solving -5x + -4x2 = 30 + 5x Solving for variable 'x'. Reorder the terms: -30 + -5x + -5x + -4x2 = 30 + 5x + -30 + -5x Combine like terms: -5x + -5x = -10x -30 + -10x + -4x2 = 30 + 5x + -30 + -5x Reorder the terms: -30 + -10x + -4x2 = 30 + -30 + 5x + -5x Combine like terms: 30 + -30 = 0 -30 + -10x + -4x2 = 0 + 5x + -5x -30 + -10x + -4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -30 + -10x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(15 + 5x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(15 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + 5x + 2x2 = 0 Solving 15 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 2.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 2.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 2.5x + x2 = 0 + -7.5 2.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 2.5x + x2 = -7.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -7.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -7.5 + 1.5625 Combine like terms: -7.5 + 1.5625 = -5.9375 1.5625 + 2.5x + x2 = -5.9375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -5.9375 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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