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Simplifying 4x2 + -32x + -76 = 0 Reorder the terms: -76 + -32x + 4x2 = 0 Solving -76 + -32x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-19 + -8x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-19 + -8x + x2)' equal to zero and attempt to solve: Simplifying -19 + -8x + x2 = 0 Solving -19 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -8x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -8x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -8x + x2 = 0 + 19 -8x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -8x + x2 = 19 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 19 + 16 Reorder the terms: 16 + -8x + x2 = 19 + 16 Combine like terms: 19 + 16 = 35 16 + -8x + x2 = 35 Factor a perfect square on the left side: (x + -4)(x + -4) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -4) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -4 = 5.916079783 Simplifying x + -4 = 5.916079783 Reorder the terms: -4 + x = 5.916079783 Solving -4 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.916079783 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.916079783 + 4 x = 5.916079783 + 4 Combine like terms: 5.916079783 + 4 = 9.916079783 x = 9.916079783 Simplifying x = 9.916079783Subproblem 2
x + -4 = -5.916079783 Simplifying x + -4 = -5.916079783 Reorder the terms: -4 + x = -5.916079783 Solving -4 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.916079783 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.916079783 + 4 x = -5.916079783 + 4 Combine like terms: -5.916079783 + 4 = -1.916079783 x = -1.916079783 Simplifying x = -1.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.916079783, -1.916079783}Solution
x = {9.916079783, -1.916079783}
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