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Simplifying 8x2 + 24x = -4x2 + -15 Reorder the terms: 24x + 8x2 = -4x2 + -15 Reorder the terms: 24x + 8x2 = -15 + -4x2 Solving 24x + 8x2 = -15 + -4x2 Solving for variable 'x'. Reorder the terms: 15 + 24x + 8x2 + 4x2 = -15 + -4x2 + 15 + 4x2 Combine like terms: 8x2 + 4x2 = 12x2 15 + 24x + 12x2 = -15 + -4x2 + 15 + 4x2 Reorder the terms: 15 + 24x + 12x2 = -15 + 15 + -4x2 + 4x2 Combine like terms: -15 + 15 = 0 15 + 24x + 12x2 = 0 + -4x2 + 4x2 15 + 24x + 12x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 15 + 24x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 8x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 8x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 8x + 4x2 = 0 Solving 5 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 2x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 2x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 2x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 2x + x2 = 0 + -1.25 2x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 2x + x2 = -1.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -1.25 + 1 Reorder the terms: 1 + 2x + x2 = -1.25 + 1 Combine like terms: -1.25 + 1 = -0.25 1 + 2x + x2 = -0.25 Factor a perfect square on the left side: (x + 1)(x + 1) = -0.25 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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