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Simplifying 7x(x + -4) + -2x(8x2 + -4x + 3) = 0 Reorder the terms: 7x(-4 + x) + -2x(8x2 + -4x + 3) = 0 (-4 * 7x + x * 7x) + -2x(8x2 + -4x + 3) = 0 (-28x + 7x2) + -2x(8x2 + -4x + 3) = 0 Reorder the terms: -28x + 7x2 + -2x(3 + -4x + 8x2) = 0 -28x + 7x2 + (3 * -2x + -4x * -2x + 8x2 * -2x) = 0 -28x + 7x2 + (-6x + 8x2 + -16x3) = 0 Reorder the terms: -28x + -6x + 7x2 + 8x2 + -16x3 = 0 Combine like terms: -28x + -6x = -34x -34x + 7x2 + 8x2 + -16x3 = 0 Combine like terms: 7x2 + 8x2 = 15x2 -34x + 15x2 + -16x3 = 0 Solving -34x + 15x2 + -16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-34 + 15x + -16x2) = 0Subproblem 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 '(-34 + 15x + -16x2)' equal to zero and attempt to solve: Simplifying -34 + 15x + -16x2 = 0 Solving -34 + 15x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 2.125 + -0.9375x + x2 = 0 Move the constant term to the right: Add '-2.125' to each side of the equation. 2.125 + -0.9375x + -2.125 + x2 = 0 + -2.125 Reorder the terms: 2.125 + -2.125 + -0.9375x + x2 = 0 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + -0.9375x + x2 = 0 + -2.125 -0.9375x + x2 = 0 + -2.125 Combine like terms: 0 + -2.125 = -2.125 -0.9375x + x2 = -2.125 The x term is -0.9375x. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375x + 0.2197265625 + x2 = -2.125 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375x + x2 = -2.125 + 0.2197265625 Combine like terms: -2.125 + 0.2197265625 = -1.9052734375 0.2197265625 + -0.9375x + x2 = -1.9052734375 Factor a perfect square on the left side: (x + -0.46875)(x + -0.46875) = -1.9052734375 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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