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Simplifying 0 = 56x2 + -72x + 144 Reorder the terms: 0 = 144 + -72x + 56x2 Solving 0 = 144 + -72x + 56x2 Solving for variable 'x'. Combine like terms: 0 + -144 = -144 -144 + 72x + -56x2 = 144 + -72x + 56x2 + -144 + 72x + -56x2 Reorder the terms: -144 + 72x + -56x2 = 144 + -144 + -72x + 72x + 56x2 + -56x2 Combine like terms: 144 + -144 = 0 -144 + 72x + -56x2 = 0 + -72x + 72x + 56x2 + -56x2 -144 + 72x + -56x2 = -72x + 72x + 56x2 + -56x2 Combine like terms: -72x + 72x = 0 -144 + 72x + -56x2 = 0 + 56x2 + -56x2 -144 + 72x + -56x2 = 56x2 + -56x2 Combine like terms: 56x2 + -56x2 = 0 -144 + 72x + -56x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-18 + 9x + -7x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-18 + 9x + -7x2)' equal to zero and attempt to solve: Simplifying -18 + 9x + -7x2 = 0 Solving -18 + 9x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 2.571428571 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '-2.571428571' to each side of the equation. 2.571428571 + -1.285714286x + -2.571428571 + x2 = 0 + -2.571428571 Reorder the terms: 2.571428571 + -2.571428571 + -1.285714286x + x2 = 0 + -2.571428571 Combine like terms: 2.571428571 + -2.571428571 = 0.000000000 0.000000000 + -1.285714286x + x2 = 0 + -2.571428571 -1.285714286x + x2 = 0 + -2.571428571 Combine like terms: 0 + -2.571428571 = -2.571428571 -1.285714286x + x2 = -2.571428571 The x term is -1.285714286x. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286x + 0.4132653063 + x2 = -2.571428571 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = -2.571428571 + 0.4132653063 Combine like terms: -2.571428571 + 0.4132653063 = -2.1581632647 0.4132653063 + -1.285714286x + x2 = -2.1581632647 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = -2.1581632647 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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