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Simplifying 0 = 8X2 + 10X + -2 Reorder the terms: 0 = -2 + 10X + 8X2 Solving 0 = -2 + 10X + 8X2 Solving for variable 'X'. Combine like terms: 0 + 2 = 2 2 + -10X + -8X2 = -2 + 10X + 8X2 + 2 + -10X + -8X2 Reorder the terms: 2 + -10X + -8X2 = -2 + 2 + 10X + -10X + 8X2 + -8X2 Combine like terms: -2 + 2 = 0 2 + -10X + -8X2 = 0 + 10X + -10X + 8X2 + -8X2 2 + -10X + -8X2 = 10X + -10X + 8X2 + -8X2 Combine like terms: 10X + -10X = 0 2 + -10X + -8X2 = 0 + 8X2 + -8X2 2 + -10X + -8X2 = 8X2 + -8X2 Combine like terms: 8X2 + -8X2 = 0 2 + -10X + -8X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -5X + -4X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -5X + -4X2)' equal to zero and attempt to solve: Simplifying 1 + -5X + -4X2 = 0 Solving 1 + -5X + -4X2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + 1.25X + X2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 1.25X + 0.25 + X2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 1.25X + X2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 1.25X + X2 = 0 + 0.25 1.25X + X2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 1.25X + X2 = 0.25 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 = 0.25 + 0.390625 Reorder the terms: 0.390625 + 1.25X + X2 = 0.25 + 0.390625 Combine like terms: 0.25 + 0.390625 = 0.640625 0.390625 + 1.25X + X2 = 0.640625 Factor a perfect square on the left side: (X + 0.625)(X + 0.625) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (X + 0.625) equal to 0.80039053 and -0.80039053.Subproblem 1
X + 0.625 = 0.80039053 Simplifying X + 0.625 = 0.80039053 Reorder the terms: 0.625 + X = 0.80039053 Solving 0.625 + X = 0.80039053 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + X = 0.80039053 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + X = 0.80039053 + -0.625 X = 0.80039053 + -0.625 Combine like terms: 0.80039053 + -0.625 = 0.17539053 X = 0.17539053 Simplifying X = 0.17539053Subproblem 2
X + 0.625 = -0.80039053 Simplifying X + 0.625 = -0.80039053 Reorder the terms: 0.625 + X = -0.80039053 Solving 0.625 + X = -0.80039053 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + X = -0.80039053 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + X = -0.80039053 + -0.625 X = -0.80039053 + -0.625 Combine like terms: -0.80039053 + -0.625 = -1.42539053 X = -1.42539053 Simplifying X = -1.42539053Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.17539053, -1.42539053}Solution
X = {0.17539053, -1.42539053}
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