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Simplifying 137x2 + -1912x + -1644 = 0 Reorder the terms: -1644 + -1912x + 137x2 = 0 Solving -1644 + -1912x + 137x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 137 the coefficient of the squared term: Divide each side by '137'. -12 + -13.95620438x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -13.95620438x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -13.95620438x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -13.95620438x + x2 = 0 + 12 -13.95620438x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -13.95620438x + x2 = 12 The x term is -13.95620438x. Take half its coefficient (-6.97810219). Square it (48.69391017) and add it to both sides. Add '48.69391017' to each side of the equation. -13.95620438x + 48.69391017 + x2 = 12 + 48.69391017 Reorder the terms: 48.69391017 + -13.95620438x + x2 = 12 + 48.69391017 Combine like terms: 12 + 48.69391017 = 60.69391017 48.69391017 + -13.95620438x + x2 = 60.69391017 Factor a perfect square on the left side: (x + -6.97810219)(x + -6.97810219) = 60.69391017 Calculate the square root of the right side: 7.790629639 Break this problem into two subproblems by setting (x + -6.97810219) equal to 7.790629639 and -7.790629639.Subproblem 1
x + -6.97810219 = 7.790629639 Simplifying x + -6.97810219 = 7.790629639 Reorder the terms: -6.97810219 + x = 7.790629639 Solving -6.97810219 + x = 7.790629639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.97810219' to each side of the equation. -6.97810219 + 6.97810219 + x = 7.790629639 + 6.97810219 Combine like terms: -6.97810219 + 6.97810219 = 0.00000000 0.00000000 + x = 7.790629639 + 6.97810219 x = 7.790629639 + 6.97810219 Combine like terms: 7.790629639 + 6.97810219 = 14.768731829 x = 14.768731829 Simplifying x = 14.768731829Subproblem 2
x + -6.97810219 = -7.790629639 Simplifying x + -6.97810219 = -7.790629639 Reorder the terms: -6.97810219 + x = -7.790629639 Solving -6.97810219 + x = -7.790629639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.97810219' to each side of the equation. -6.97810219 + 6.97810219 + x = -7.790629639 + 6.97810219 Combine like terms: -6.97810219 + 6.97810219 = 0.00000000 0.00000000 + x = -7.790629639 + 6.97810219 x = -7.790629639 + 6.97810219 Combine like terms: -7.790629639 + 6.97810219 = -0.812527449 x = -0.812527449 Simplifying x = -0.812527449Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.768731829, -0.812527449}
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