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Simplifying (-12x2 + 6x) + -1(5x2 + 7x + -1) = 0 Reorder the terms: (6x + -12x2) + -1(5x2 + 7x + -1) = 0 Remove parenthesis around (6x + -12x2) 6x + -12x2 + -1(5x2 + 7x + -1) = 0 Reorder the terms: 6x + -12x2 + -1(-1 + 7x + 5x2) = 0 6x + -12x2 + (-1 * -1 + 7x * -1 + 5x2 * -1) = 0 6x + -12x2 + (1 + -7x + -5x2) = 0 Reorder the terms: 1 + 6x + -7x + -12x2 + -5x2 = 0 Combine like terms: 6x + -7x = -1x 1 + -1x + -12x2 + -5x2 = 0 Combine like terms: -12x2 + -5x2 = -17x2 1 + -1x + -17x2 = 0 Solving 1 + -1x + -17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -0.05882352941 + 0.05882352941x + x2 = 0 Move the constant term to the right: Add '0.05882352941' to each side of the equation. -0.05882352941 + 0.05882352941x + 0.05882352941 + x2 = 0 + 0.05882352941 Reorder the terms: -0.05882352941 + 0.05882352941 + 0.05882352941x + x2 = 0 + 0.05882352941 Combine like terms: -0.05882352941 + 0.05882352941 = 0.00000000000 0.00000000000 + 0.05882352941x + x2 = 0 + 0.05882352941 0.05882352941x + x2 = 0 + 0.05882352941 Combine like terms: 0 + 0.05882352941 = 0.05882352941 0.05882352941x + x2 = 0.05882352941 The x term is 0.05882352941x. Take half its coefficient (0.02941176471). Square it (0.0008650519034) and add it to both sides. Add '0.0008650519034' to each side of the equation. 0.05882352941x + 0.0008650519034 + x2 = 0.05882352941 + 0.0008650519034 Reorder the terms: 0.0008650519034 + 0.05882352941x + x2 = 0.05882352941 + 0.0008650519034 Combine like terms: 0.05882352941 + 0.0008650519034 = 0.0596885813134 0.0008650519034 + 0.05882352941x + x2 = 0.0596885813134 Factor a perfect square on the left side: (x + 0.02941176471)(x + 0.02941176471) = 0.0596885813134 Calculate the square root of the right side: 0.244312467 Break this problem into two subproblems by setting (x + 0.02941176471) equal to 0.244312467 and -0.244312467.Subproblem 1
x + 0.02941176471 = 0.244312467 Simplifying x + 0.02941176471 = 0.244312467 Reorder the terms: 0.02941176471 + x = 0.244312467 Solving 0.02941176471 + x = 0.244312467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02941176471' to each side of the equation. 0.02941176471 + -0.02941176471 + x = 0.244312467 + -0.02941176471 Combine like terms: 0.02941176471 + -0.02941176471 = 0.00000000000 0.00000000000 + x = 0.244312467 + -0.02941176471 x = 0.244312467 + -0.02941176471 Combine like terms: 0.244312467 + -0.02941176471 = 0.21490070229 x = 0.21490070229 Simplifying x = 0.21490070229Subproblem 2
x + 0.02941176471 = -0.244312467 Simplifying x + 0.02941176471 = -0.244312467 Reorder the terms: 0.02941176471 + x = -0.244312467 Solving 0.02941176471 + x = -0.244312467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02941176471' to each side of the equation. 0.02941176471 + -0.02941176471 + x = -0.244312467 + -0.02941176471 Combine like terms: 0.02941176471 + -0.02941176471 = 0.00000000000 0.00000000000 + x = -0.244312467 + -0.02941176471 x = -0.244312467 + -0.02941176471 Combine like terms: -0.244312467 + -0.02941176471 = -0.27372423171 x = -0.27372423171 Simplifying x = -0.27372423171Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.21490070229, -0.27372423171}
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