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Simplifying 6x2 + -60x + 114 = 0 Reorder the terms: 114 + -60x + 6x2 = 0 Solving 114 + -60x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(19 + -10x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(19 + -10x + x2)' equal to zero and attempt to solve: Simplifying 19 + -10x + x2 = 0 Solving 19 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -10x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -10x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -10x + x2 = 0 + -19 -10x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -10x + x2 = -19 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -19 + 25 Reorder the terms: 25 + -10x + x2 = -19 + 25 Combine like terms: -19 + 25 = 6 25 + -10x + x2 = 6 Factor a perfect square on the left side: (x + -5)(x + -5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -5) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -5 = 2.449489743 Simplifying x + -5 = 2.449489743 Reorder the terms: -5 + x = 2.449489743 Solving -5 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.449489743 + 5 x = 2.449489743 + 5 Combine like terms: 2.449489743 + 5 = 7.449489743 x = 7.449489743 Simplifying x = 7.449489743Subproblem 2
x + -5 = -2.449489743 Simplifying x + -5 = -2.449489743 Reorder the terms: -5 + x = -2.449489743 Solving -5 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.449489743 + 5 x = -2.449489743 + 5 Combine like terms: -2.449489743 + 5 = 2.550510257 x = 2.550510257 Simplifying x = 2.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.449489743, 2.550510257}Solution
x = {7.449489743, 2.550510257}
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