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Simplifying 0.215x2 + -2.86x + 9.42 = 0 Reorder the terms: 9.42 + -2.86x + 0.215x2 = 0 Solving 9.42 + -2.86x + 0.215x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.215 the coefficient of the squared term: Divide each side by '0.215'. 43.81395349 + -13.30232558x + x2 = 0 Move the constant term to the right: Add '-43.81395349' to each side of the equation. 43.81395349 + -13.30232558x + -43.81395349 + x2 = 0 + -43.81395349 Reorder the terms: 43.81395349 + -43.81395349 + -13.30232558x + x2 = 0 + -43.81395349 Combine like terms: 43.81395349 + -43.81395349 = 0.00000000 0.00000000 + -13.30232558x + x2 = 0 + -43.81395349 -13.30232558x + x2 = 0 + -43.81395349 Combine like terms: 0 + -43.81395349 = -43.81395349 -13.30232558x + x2 = -43.81395349 The x term is -13.30232558x. Take half its coefficient (-6.65116279). Square it (44.23796646) and add it to both sides. Add '44.23796646' to each side of the equation. -13.30232558x + 44.23796646 + x2 = -43.81395349 + 44.23796646 Reorder the terms: 44.23796646 + -13.30232558x + x2 = -43.81395349 + 44.23796646 Combine like terms: -43.81395349 + 44.23796646 = 0.42401297 44.23796646 + -13.30232558x + x2 = 0.42401297 Factor a perfect square on the left side: (x + -6.65116279)(x + -6.65116279) = 0.42401297 Calculate the square root of the right side: 0.651162783 Break this problem into two subproblems by setting (x + -6.65116279) equal to 0.651162783 and -0.651162783.Subproblem 1
x + -6.65116279 = 0.651162783 Simplifying x + -6.65116279 = 0.651162783 Reorder the terms: -6.65116279 + x = 0.651162783 Solving -6.65116279 + x = 0.651162783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.65116279' to each side of the equation. -6.65116279 + 6.65116279 + x = 0.651162783 + 6.65116279 Combine like terms: -6.65116279 + 6.65116279 = 0.00000000 0.00000000 + x = 0.651162783 + 6.65116279 x = 0.651162783 + 6.65116279 Combine like terms: 0.651162783 + 6.65116279 = 7.302325573 x = 7.302325573 Simplifying x = 7.302325573Subproblem 2
x + -6.65116279 = -0.651162783 Simplifying x + -6.65116279 = -0.651162783 Reorder the terms: -6.65116279 + x = -0.651162783 Solving -6.65116279 + x = -0.651162783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.65116279' to each side of the equation. -6.65116279 + 6.65116279 + x = -0.651162783 + 6.65116279 Combine like terms: -6.65116279 + 6.65116279 = 0.00000000 0.00000000 + x = -0.651162783 + 6.65116279 x = -0.651162783 + 6.65116279 Combine like terms: -0.651162783 + 6.65116279 = 6.000000007 x = 6.000000007 Simplifying x = 6.000000007Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.302325573, 6.000000007}
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