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Simplifying 2x2 + -18x2 + -8x + 72 = 0 Reorder the terms: 72 + -8x + 2x2 + -18x2 = 0 Combine like terms: 2x2 + -18x2 = -16x2 72 + -8x + -16x2 = 0 Solving 72 + -8x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(9 + -1x + -2x2) = 0 Ignore the factor 8.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 = 1.886000936 x = 1.886000936 Simplifying x = 1.886000936Subproblem 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 = -2.386000936 x = -2.386000936 Simplifying x = -2.386000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.886000936, -2.386000936}Solution
x = {1.886000936, -2.386000936}
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