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Simplifying -4(4x2 + -8x + 15) = 0 Reorder the terms: -4(15 + -8x + 4x2) = 0 (15 * -4 + -8x * -4 + 4x2 * -4) = 0 (-60 + 32x + -16x2) = 0 Solving -60 + 32x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 8x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + 8x + -4x2)' equal to zero and attempt to solve: Simplifying -15 + 8x + -4x2 = 0 Solving -15 + 8x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.75 + -2x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -2x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -2x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -2x + x2 = 0 + -3.75 -2x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -2x + x2 = -3.75 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 = -3.75 + 1 Reorder the terms: 1 + -2x + x2 = -3.75 + 1 Combine like terms: -3.75 + 1 = -2.75 1 + -2x + x2 = -2.75 Factor a perfect square on the left side: (x + -1)(x + -1) = -2.75 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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