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Simplifying 4x4 = 5x3 + -7x2 Reorder the terms: 4x4 = -7x2 + 5x3 Solving 4x4 = -7x2 + 5x3 Solving for variable 'x'. Reorder the terms: 7x2 + -5x3 + 4x4 = -7x2 + 5x3 + 7x2 + -5x3 Reorder the terms: 7x2 + -5x3 + 4x4 = -7x2 + 7x2 + 5x3 + -5x3 Combine like terms: -7x2 + 7x2 = 0 7x2 + -5x3 + 4x4 = 0 + 5x3 + -5x3 7x2 + -5x3 + 4x4 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 7x2 + -5x3 + 4x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(7 + -5x + 4x2) = 0Subproblem 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 '(7 + -5x + 4x2)' equal to zero and attempt to solve: Simplifying 7 + -5x + 4x2 = 0 Solving 7 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -1.25x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -1.25x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -1.25x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -1.25x + x2 = 0 + -1.75 -1.25x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -1.25x + x2 = -1.75 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -1.75 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -1.75 + 0.390625 Combine like terms: -1.75 + 0.390625 = -1.359375 0.390625 + -1.25x + x2 = -1.359375 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = -1.359375 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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