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Simplifying 8x2(-7x2 + 6x + -8) = 0 Reorder the terms: 8x2(-8 + 6x + -7x2) = 0 (-8 * 8x2 + 6x * 8x2 + -7x2 * 8x2) = 0 (-64x2 + 48x3 + -56x4) = 0 Solving -64x2 + 48x3 + -56x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x2'. 8x2(-8 + 6x + -7x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-8 + 6x + -7x2)' equal to zero and attempt to solve: Simplifying -8 + 6x + -7x2 = 0 Solving -8 + 6x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 1.142857143 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + -0.8571428571x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + -0.8571428571x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + -0.8571428571x + x2 = 0 + -1.142857143 -0.8571428571x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 -0.8571428571x + x2 = -1.142857143 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = -1.142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = -1.142857143 + 0.1836734694 Combine like terms: -1.142857143 + 0.1836734694 = -0.9591836736 0.1836734694 + -0.8571428571x + x2 = -0.9591836736 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = -0.9591836736 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.Solution
x = {0}
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