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Simplifying 0 = 8x2 + 6x + 30 Reorder the terms: 0 = 30 + 6x + 8x2 Solving 0 = 30 + 6x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + -6x + -8x2 = 30 + 6x + 8x2 + -30 + -6x + -8x2 Reorder the terms: -30 + -6x + -8x2 = 30 + -30 + 6x + -6x + 8x2 + -8x2 Combine like terms: 30 + -30 = 0 -30 + -6x + -8x2 = 0 + 6x + -6x + 8x2 + -8x2 -30 + -6x + -8x2 = 6x + -6x + 8x2 + -8x2 Combine like terms: 6x + -6x = 0 -30 + -6x + -8x2 = 0 + 8x2 + -8x2 -30 + -6x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -30 + -6x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(15 + 3x + 4x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(15 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 15 + 3x + 4x2 = 0 Solving 15 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 0.75x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 0.75x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 0.75x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 0.75x + x2 = 0 + -3.75 0.75x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 0.75x + x2 = -3.75 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -3.75 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -3.75 + 0.140625 Combine like terms: -3.75 + 0.140625 = -3.609375 0.140625 + 0.75x + x2 = -3.609375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -3.609375 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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