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Simplifying 10x2 + 86x + 12 = 0 Reorder the terms: 12 + 86x + 10x2 = 0 Solving 12 + 86x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 43x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 43x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + 43x + 5x2 = 0 Solving 6 + 43x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + 8.6x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 8.6x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 8.6x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 8.6x + x2 = 0 + -1.2 8.6x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 8.6x + x2 = -1.2 The x term is 8.6x. Take half its coefficient (4.3). Square it (18.49) and add it to both sides. Add '18.49' to each side of the equation. 8.6x + 18.49 + x2 = -1.2 + 18.49 Reorder the terms: 18.49 + 8.6x + x2 = -1.2 + 18.49 Combine like terms: -1.2 + 18.49 = 17.29 18.49 + 8.6x + x2 = 17.29 Factor a perfect square on the left side: (x + 4.3)(x + 4.3) = 17.29 Calculate the square root of the right side: 4.158124577 Break this problem into two subproblems by setting (x + 4.3) equal to 4.158124577 and -4.158124577.Subproblem 1
x + 4.3 = 4.158124577 Simplifying x + 4.3 = 4.158124577 Reorder the terms: 4.3 + x = 4.158124577 Solving 4.3 + x = 4.158124577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.3' to each side of the equation. 4.3 + -4.3 + x = 4.158124577 + -4.3 Combine like terms: 4.3 + -4.3 = 0.0 0.0 + x = 4.158124577 + -4.3 x = 4.158124577 + -4.3 Combine like terms: 4.158124577 + -4.3 = -0.141875423 x = -0.141875423 Simplifying x = -0.141875423Subproblem 2
x + 4.3 = -4.158124577 Simplifying x + 4.3 = -4.158124577 Reorder the terms: 4.3 + x = -4.158124577 Solving 4.3 + x = -4.158124577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.3' to each side of the equation. 4.3 + -4.3 + x = -4.158124577 + -4.3 Combine like terms: 4.3 + -4.3 = 0.0 0.0 + x = -4.158124577 + -4.3 x = -4.158124577 + -4.3 Combine like terms: -4.158124577 + -4.3 = -8.458124577 x = -8.458124577 Simplifying x = -8.458124577Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.141875423, -8.458124577}Solution
x = {-0.141875423, -8.458124577}
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