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Simplifying 12x2 + 10x = 10 Reorder the terms: 10x + 12x2 = 10 Solving 10x + 12x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 10x + 12x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 10x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 5x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying -5 + 5x + 6x2 = 0 Solving -5 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 0.8333333333x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 0.8333333333x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 0.8333333333x + x2 = 0 + 0.8333333333 0.8333333333x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 0.8333333333x + x2 = 0.8333333333 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 0.8333333333 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 0.8333333333 + 0.1736111111 Combine like terms: 0.8333333333 + 0.1736111111 = 1.0069444444 0.1736111111 + 0.8333333333x + x2 = 1.0069444444 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 1.0069444444 Calculate the square root of the right side: 1.003466215 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 1.003466215 and -1.003466215.Subproblem 1
x + 0.4166666667 = 1.003466215 Simplifying x + 0.4166666667 = 1.003466215 Reorder the terms: 0.4166666667 + x = 1.003466215 Solving 0.4166666667 + x = 1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 1.003466215 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 1.003466215 + -0.4166666667 x = 1.003466215 + -0.4166666667 Combine like terms: 1.003466215 + -0.4166666667 = 0.5867995483 x = 0.5867995483 Simplifying x = 0.5867995483Subproblem 2
x + 0.4166666667 = -1.003466215 Simplifying x + 0.4166666667 = -1.003466215 Reorder the terms: 0.4166666667 + x = -1.003466215 Solving 0.4166666667 + x = -1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -1.003466215 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -1.003466215 + -0.4166666667 x = -1.003466215 + -0.4166666667 Combine like terms: -1.003466215 + -0.4166666667 = -1.4201328817 x = -1.4201328817 Simplifying x = -1.4201328817Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5867995483, -1.4201328817}Solution
x = {0.5867995483, -1.4201328817}
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