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Simplifying 0 = 27.2551x + 4.9x2 + -11.91 Reorder the terms: 0 = -11.91 + 27.2551x + 4.9x2 Solving 0 = -11.91 + 27.2551x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 11.91 = 11.91 11.91 + -27.2551x + -4.9x2 = -11.91 + 27.2551x + 4.9x2 + 11.91 + -27.2551x + -4.9x2 Reorder the terms: 11.91 + -27.2551x + -4.9x2 = -11.91 + 11.91 + 27.2551x + -27.2551x + 4.9x2 + -4.9x2 Combine like terms: -11.91 + 11.91 = 0.00 11.91 + -27.2551x + -4.9x2 = 0.00 + 27.2551x + -27.2551x + 4.9x2 + -4.9x2 11.91 + -27.2551x + -4.9x2 = 27.2551x + -27.2551x + 4.9x2 + -4.9x2 Combine like terms: 27.2551x + -27.2551x = 0.0000 11.91 + -27.2551x + -4.9x2 = 0.0000 + 4.9x2 + -4.9x2 11.91 + -27.2551x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 11.91 + -27.2551x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.430612245 + 5.562265306x + x2 = 0 Move the constant term to the right: Add '2.430612245' to each side of the equation. -2.430612245 + 5.562265306x + 2.430612245 + x2 = 0 + 2.430612245 Reorder the terms: -2.430612245 + 2.430612245 + 5.562265306x + x2 = 0 + 2.430612245 Combine like terms: -2.430612245 + 2.430612245 = 0.000000000 0.000000000 + 5.562265306x + x2 = 0 + 2.430612245 5.562265306x + x2 = 0 + 2.430612245 Combine like terms: 0 + 2.430612245 = 2.430612245 5.562265306x + x2 = 2.430612245 The x term is 5.562265306x. Take half its coefficient (2.781132653). Square it (7.734698834) and add it to both sides. Add '7.734698834' to each side of the equation. 5.562265306x + 7.734698834 + x2 = 2.430612245 + 7.734698834 Reorder the terms: 7.734698834 + 5.562265306x + x2 = 2.430612245 + 7.734698834 Combine like terms: 2.430612245 + 7.734698834 = 10.165311079 7.734698834 + 5.562265306x + x2 = 10.165311079 Factor a perfect square on the left side: (x + 2.781132653)(x + 2.781132653) = 10.165311079 Calculate the square root of the right side: 3.188308498 Break this problem into two subproblems by setting (x + 2.781132653) equal to 3.188308498 and -3.188308498.Subproblem 1
x + 2.781132653 = 3.188308498 Simplifying x + 2.781132653 = 3.188308498 Reorder the terms: 2.781132653 + x = 3.188308498 Solving 2.781132653 + x = 3.188308498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.781132653' to each side of the equation. 2.781132653 + -2.781132653 + x = 3.188308498 + -2.781132653 Combine like terms: 2.781132653 + -2.781132653 = 0.000000000 0.000000000 + x = 3.188308498 + -2.781132653 x = 3.188308498 + -2.781132653 Combine like terms: 3.188308498 + -2.781132653 = 0.407175845 x = 0.407175845 Simplifying x = 0.407175845Subproblem 2
x + 2.781132653 = -3.188308498 Simplifying x + 2.781132653 = -3.188308498 Reorder the terms: 2.781132653 + x = -3.188308498 Solving 2.781132653 + x = -3.188308498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.781132653' to each side of the equation. 2.781132653 + -2.781132653 + x = -3.188308498 + -2.781132653 Combine like terms: 2.781132653 + -2.781132653 = 0.000000000 0.000000000 + x = -3.188308498 + -2.781132653 x = -3.188308498 + -2.781132653 Combine like terms: -3.188308498 + -2.781132653 = -5.969441151 x = -5.969441151 Simplifying x = -5.969441151Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.407175845, -5.969441151}
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