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Simplifying 8x(7x2 + -3x + 8) = 0 Reorder the terms: 8x(8 + -3x + 7x2) = 0 (8 * 8x + -3x * 8x + 7x2 * 8x) = 0 (64x + -24x2 + 56x3) = 0 Solving 64x + -24x2 + 56x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x'. 8x(8 + -3x + 7x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(8 + -3x + 7x2)' equal to zero and attempt to solve: Simplifying 8 + -3x + 7x2 = 0 Solving 8 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.142857143 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + -0.4285714286x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + -0.4285714286x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + -1.142857143 -0.4285714286x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 -0.4285714286x + x2 = -1.142857143 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = -1.142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = -1.142857143 + 0.04591836735 Combine like terms: -1.142857143 + 0.04591836735 = -1.09693877565 0.04591836735 + -0.4285714286x + x2 = -1.09693877565 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = -1.09693877565 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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