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Simplifying 12x2 + -100x + 156 = 0 Reorder the terms: 156 + -100x + 12x2 = 0 Solving 156 + -100x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(39 + -25x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(39 + -25x + 3x2)' equal to zero and attempt to solve: Simplifying 39 + -25x + 3x2 = 0 Solving 39 + -25x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 13 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8.333333333x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -8.333333333x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8.333333333x + x2 = 0 + -13 -8.333333333x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8.333333333x + x2 = -13 The x term is -8.333333333x. Take half its coefficient (-4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. -8.333333333x + 17.36111111 + x2 = -13 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = -13 + 17.36111111 Combine like terms: -13 + 17.36111111 = 4.36111111 17.36111111 + -8.333333333x + x2 = 4.36111111 Factor a perfect square on the left side: (x + -4.166666667)(x + -4.166666667) = 4.36111111 Calculate the square root of the right side: 2.088327347 Break this problem into two subproblems by setting (x + -4.166666667) equal to 2.088327347 and -2.088327347.Subproblem 1
x + -4.166666667 = 2.088327347 Simplifying x + -4.166666667 = 2.088327347 Reorder the terms: -4.166666667 + x = 2.088327347 Solving -4.166666667 + x = 2.088327347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 2.088327347 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 2.088327347 + 4.166666667 x = 2.088327347 + 4.166666667 Combine like terms: 2.088327347 + 4.166666667 = 6.254994014 x = 6.254994014 Simplifying x = 6.254994014Subproblem 2
x + -4.166666667 = -2.088327347 Simplifying x + -4.166666667 = -2.088327347 Reorder the terms: -4.166666667 + x = -2.088327347 Solving -4.166666667 + x = -2.088327347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -2.088327347 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -2.088327347 + 4.166666667 x = -2.088327347 + 4.166666667 Combine like terms: -2.088327347 + 4.166666667 = 2.07833932 x = 2.07833932 Simplifying x = 2.07833932Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.254994014, 2.07833932}Solution
x = {6.254994014, 2.07833932}
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