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Simplifying 0 = 4x2 + 72x + 191 Reorder the terms: 0 = 191 + 72x + 4x2 Solving 0 = 191 + 72x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -191 = -191 -191 + -72x + -4x2 = 191 + 72x + 4x2 + -191 + -72x + -4x2 Reorder the terms: -191 + -72x + -4x2 = 191 + -191 + 72x + -72x + 4x2 + -4x2 Combine like terms: 191 + -191 = 0 -191 + -72x + -4x2 = 0 + 72x + -72x + 4x2 + -4x2 -191 + -72x + -4x2 = 72x + -72x + 4x2 + -4x2 Combine like terms: 72x + -72x = 0 -191 + -72x + -4x2 = 0 + 4x2 + -4x2 -191 + -72x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -191 + -72x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(191 + 72x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(191 + 72x + 4x2)' equal to zero and attempt to solve: Simplifying 191 + 72x + 4x2 = 0 Solving 191 + 72x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 47.75 + 18x + x2 = 0 Move the constant term to the right: Add '-47.75' to each side of the equation. 47.75 + 18x + -47.75 + x2 = 0 + -47.75 Reorder the terms: 47.75 + -47.75 + 18x + x2 = 0 + -47.75 Combine like terms: 47.75 + -47.75 = 0.00 0.00 + 18x + x2 = 0 + -47.75 18x + x2 = 0 + -47.75 Combine like terms: 0 + -47.75 = -47.75 18x + x2 = -47.75 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -47.75 + 81 Reorder the terms: 81 + 18x + x2 = -47.75 + 81 Combine like terms: -47.75 + 81 = 33.25 81 + 18x + x2 = 33.25 Factor a perfect square on the left side: (x + 9)(x + 9) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + 9) equal to 5.766281297 and -5.766281297.Subproblem 1
x + 9 = 5.766281297 Simplifying x + 9 = 5.766281297 Reorder the terms: 9 + x = 5.766281297 Solving 9 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 5.766281297 + -9 Combine like terms: 9 + -9 = 0 0 + x = 5.766281297 + -9 x = 5.766281297 + -9 Combine like terms: 5.766281297 + -9 = -3.233718703 x = -3.233718703 Simplifying x = -3.233718703Subproblem 2
x + 9 = -5.766281297 Simplifying x + 9 = -5.766281297 Reorder the terms: 9 + x = -5.766281297 Solving 9 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -5.766281297 + -9 Combine like terms: 9 + -9 = 0 0 + x = -5.766281297 + -9 x = -5.766281297 + -9 Combine like terms: -5.766281297 + -9 = -14.766281297 x = -14.766281297 Simplifying x = -14.766281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.233718703, -14.766281297}Solution
x = {-3.233718703, -14.766281297}
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