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Simplifying 4x2 + -2x + -18 = 0 Reorder the terms: -18 + -2x + 4x2 = 0 Solving -18 + -2x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -9 + -1x + 2x2 = 0 Solving -9 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -0.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -0.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -0.5x + x2 = 0 + 4.5 -0.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -0.5x + x2 = 4.5 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 = 4.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 4.5 + 0.0625 Combine like terms: 4.5 + 0.0625 = 4.5625 0.0625 + -0.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -0.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + -0.25 = 2.136000936 Simplifying x + -0.25 = 2.136000936 Reorder the terms: -0.25 + x = 2.136000936 Solving -0.25 + x = 2.136000936 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 = 2.136000936 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.136000936 + 0.25 x = 2.136000936 + 0.25 Combine like terms: 2.136000936 + 0.25 = 2.386000936 x = 2.386000936 Simplifying x = 2.386000936Subproblem 2
x + -0.25 = -2.136000936 Simplifying x + -0.25 = -2.136000936 Reorder the terms: -0.25 + x = -2.136000936 Solving -0.25 + x = -2.136000936 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 = -2.136000936 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.136000936 + 0.25 x = -2.136000936 + 0.25 Combine like terms: -2.136000936 + 0.25 = -1.886000936 x = -1.886000936 Simplifying x = -1.886000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.386000936, -1.886000936}Solution
x = {2.386000936, -1.886000936}
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