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Simplifying 8x2 + 4x + -150 = 0 Reorder the terms: -150 + 4x + 8x2 = 0 Solving -150 + 4x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 2x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying -75 + 2x + 4x2 = 0 Solving -75 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.75 + 0.5x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + 0.5x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + 0.5x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + 0.5x + x2 = 0 + 18.75 0.5x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 0.5x + x2 = 18.75 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 18.75 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 18.75 + 0.0625 Combine like terms: 18.75 + 0.0625 = 18.8125 0.0625 + 0.5x + x2 = 18.8125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 18.8125 Calculate the square root of the right side: 4.337337893 Break this problem into two subproblems by setting (x + 0.25) equal to 4.337337893 and -4.337337893.Subproblem 1
x + 0.25 = 4.337337893 Simplifying x + 0.25 = 4.337337893 Reorder the terms: 0.25 + x = 4.337337893 Solving 0.25 + x = 4.337337893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 4.337337893 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.337337893 + -0.25 x = 4.337337893 + -0.25 Combine like terms: 4.337337893 + -0.25 = 4.087337893 x = 4.087337893 Simplifying x = 4.087337893Subproblem 2
x + 0.25 = -4.337337893 Simplifying x + 0.25 = -4.337337893 Reorder the terms: 0.25 + x = -4.337337893 Solving 0.25 + x = -4.337337893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -4.337337893 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.337337893 + -0.25 x = -4.337337893 + -0.25 Combine like terms: -4.337337893 + -0.25 = -4.587337893 x = -4.587337893 Simplifying x = -4.587337893Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.087337893, -4.587337893}Solution
x = {4.087337893, -4.587337893}
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