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Simplifying 10x4 = -32x3 + -32x2 Reorder the terms: 10x4 = -32x2 + -32x3 Solving 10x4 = -32x2 + -32x3 Solving for variable 'x'. Reorder the terms: 32x2 + 32x3 + 10x4 = -32x2 + -32x3 + 32x2 + 32x3 Reorder the terms: 32x2 + 32x3 + 10x4 = -32x2 + 32x2 + -32x3 + 32x3 Combine like terms: -32x2 + 32x2 = 0 32x2 + 32x3 + 10x4 = 0 + -32x3 + 32x3 32x2 + 32x3 + 10x4 = -32x3 + 32x3 Combine like terms: -32x3 + 32x3 = 0 32x2 + 32x3 + 10x4 = 0 Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(16 + 16x + 5x2) = 0 Ignore the factor 2.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 '(16 + 16x + 5x2)' equal to zero and attempt to solve: Simplifying 16 + 16x + 5x2 = 0 Solving 16 + 16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + 3.2x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + 3.2x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + 3.2x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + 3.2x + x2 = 0 + -3.2 3.2x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 3.2x + x2 = -3.2 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = -3.2 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = -3.2 + 2.56 Combine like terms: -3.2 + 2.56 = -0.64 2.56 + 3.2x + x2 = -0.64 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = -0.64 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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