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Simplifying 12x2 + -77x + 15 = 0 Reorder the terms: 15 + -77x + 12x2 = 0 Solving 15 + -77x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.25 + -6.416666667x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -6.416666667x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -6.416666667x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -6.416666667x + x2 = 0 + -1.25 -6.416666667x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -6.416666667x + x2 = -1.25 The x term is -6.416666667x. Take half its coefficient (-3.208333334). Square it (10.29340278) and add it to both sides. Add '10.29340278' to each side of the equation. -6.416666667x + 10.29340278 + x2 = -1.25 + 10.29340278 Reorder the terms: 10.29340278 + -6.416666667x + x2 = -1.25 + 10.29340278 Combine like terms: -1.25 + 10.29340278 = 9.04340278 10.29340278 + -6.416666667x + x2 = 9.04340278 Factor a perfect square on the left side: (x + -3.208333334)(x + -3.208333334) = 9.04340278 Calculate the square root of the right side: 3.007225096 Break this problem into two subproblems by setting (x + -3.208333334) equal to 3.007225096 and -3.007225096.Subproblem 1
x + -3.208333334 = 3.007225096 Simplifying x + -3.208333334 = 3.007225096 Reorder the terms: -3.208333334 + x = 3.007225096 Solving -3.208333334 + x = 3.007225096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.208333334' to each side of the equation. -3.208333334 + 3.208333334 + x = 3.007225096 + 3.208333334 Combine like terms: -3.208333334 + 3.208333334 = 0.000000000 0.000000000 + x = 3.007225096 + 3.208333334 x = 3.007225096 + 3.208333334 Combine like terms: 3.007225096 + 3.208333334 = 6.21555843 x = 6.21555843 Simplifying x = 6.21555843Subproblem 2
x + -3.208333334 = -3.007225096 Simplifying x + -3.208333334 = -3.007225096 Reorder the terms: -3.208333334 + x = -3.007225096 Solving -3.208333334 + x = -3.007225096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.208333334' to each side of the equation. -3.208333334 + 3.208333334 + x = -3.007225096 + 3.208333334 Combine like terms: -3.208333334 + 3.208333334 = 0.000000000 0.000000000 + x = -3.007225096 + 3.208333334 x = -3.007225096 + 3.208333334 Combine like terms: -3.007225096 + 3.208333334 = 0.201108238 x = 0.201108238 Simplifying x = 0.201108238Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.21555843, 0.201108238}
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