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Simplifying 4x2 + 74x + -8 = 0 Reorder the terms: -8 + 74x + 4x2 = 0 Solving -8 + 74x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 37x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 37x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + 37x + 2x2 = 0 Solving -4 + 37x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 18.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 18.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 18.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 18.5x + x2 = 0 + 2 18.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 18.5x + x2 = 2 The x term is 18.5x. Take half its coefficient (9.25). Square it (85.5625) and add it to both sides. Add '85.5625' to each side of the equation. 18.5x + 85.5625 + x2 = 2 + 85.5625 Reorder the terms: 85.5625 + 18.5x + x2 = 2 + 85.5625 Combine like terms: 2 + 85.5625 = 87.5625 85.5625 + 18.5x + x2 = 87.5625 Factor a perfect square on the left side: (x + 9.25)(x + 9.25) = 87.5625 Calculate the square root of the right side: 9.357483636 Break this problem into two subproblems by setting (x + 9.25) equal to 9.357483636 and -9.357483636.Subproblem 1
x + 9.25 = 9.357483636 Simplifying x + 9.25 = 9.357483636 Reorder the terms: 9.25 + x = 9.357483636 Solving 9.25 + x = 9.357483636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + x = 9.357483636 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = 9.357483636 + -9.25 x = 9.357483636 + -9.25 Combine like terms: 9.357483636 + -9.25 = 0.107483636 x = 0.107483636 Simplifying x = 0.107483636Subproblem 2
x + 9.25 = -9.357483636 Simplifying x + 9.25 = -9.357483636 Reorder the terms: 9.25 + x = -9.357483636 Solving 9.25 + x = -9.357483636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + x = -9.357483636 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = -9.357483636 + -9.25 x = -9.357483636 + -9.25 Combine like terms: -9.357483636 + -9.25 = -18.607483636 x = -18.607483636 Simplifying x = -18.607483636Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.107483636, -18.607483636}Solution
x = {0.107483636, -18.607483636}
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