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Simplifying 204x2 + 714x + -12 = 0 Reorder the terms: -12 + 714x + 204x2 = 0 Solving -12 + 714x + 204x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + 119x + 34x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + 119x + 34x2)' equal to zero and attempt to solve: Simplifying -2 + 119x + 34x2 = 0 Solving -2 + 119x + 34x2 = 0 Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -0.05882352941 + 3.5x + x2 = 0 Move the constant term to the right: Add '0.05882352941' to each side of the equation. -0.05882352941 + 3.5x + 0.05882352941 + x2 = 0 + 0.05882352941 Reorder the terms: -0.05882352941 + 0.05882352941 + 3.5x + x2 = 0 + 0.05882352941 Combine like terms: -0.05882352941 + 0.05882352941 = 0.00000000000 0.00000000000 + 3.5x + x2 = 0 + 0.05882352941 3.5x + x2 = 0 + 0.05882352941 Combine like terms: 0 + 0.05882352941 = 0.05882352941 3.5x + x2 = 0.05882352941 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 0.05882352941 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 0.05882352941 + 3.0625 Combine like terms: 0.05882352941 + 3.0625 = 3.12132352941 3.0625 + 3.5x + x2 = 3.12132352941 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 3.12132352941 Calculate the square root of the right side: 1.766726784 Break this problem into two subproblems by setting (x + 1.75) equal to 1.766726784 and -1.766726784.Subproblem 1
x + 1.75 = 1.766726784 Simplifying x + 1.75 = 1.766726784 Reorder the terms: 1.75 + x = 1.766726784 Solving 1.75 + x = 1.766726784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.766726784 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.766726784 + -1.75 x = 1.766726784 + -1.75 Combine like terms: 1.766726784 + -1.75 = 0.016726784 x = 0.016726784 Simplifying x = 0.016726784Subproblem 2
x + 1.75 = -1.766726784 Simplifying x + 1.75 = -1.766726784 Reorder the terms: 1.75 + x = -1.766726784 Solving 1.75 + x = -1.766726784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.766726784 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.766726784 + -1.75 x = -1.766726784 + -1.75 Combine like terms: -1.766726784 + -1.75 = -3.516726784 x = -3.516726784 Simplifying x = -3.516726784Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.016726784, -3.516726784}Solution
x = {0.016726784, -3.516726784}
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