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Simplifying -50 = -10.8x + -4.9x2 Solving -50 = -10.8x + -4.9x2 Solving for variable 'x'. Reorder the terms: -50 + 10.8x + 4.9x2 = -10.8x + 10.8x + -4.9x2 + 4.9x2 Combine like terms: -10.8x + 10.8x = 0.0 -50 + 10.8x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -50 + 10.8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -50 + 10.8x + 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'. -10.20408163 + 2.204081633x + x2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 2.204081633x + 10.20408163 + x2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 2.204081633x + x2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 2.204081633x + x2 = 0 + 10.20408163 2.204081633x + x2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 2.204081633x + x2 = 10.20408163 The x term is 2.204081633x. Take half its coefficient (1.102040817). Square it (1.214493962) and add it to both sides. Add '1.214493962' to each side of the equation. 2.204081633x + 1.214493962 + x2 = 10.20408163 + 1.214493962 Reorder the terms: 1.214493962 + 2.204081633x + x2 = 10.20408163 + 1.214493962 Combine like terms: 10.20408163 + 1.214493962 = 11.418575592 1.214493962 + 2.204081633x + x2 = 11.418575592 Factor a perfect square on the left side: (x + 1.102040817)(x + 1.102040817) = 11.418575592 Calculate the square root of the right side: 3.379138291 Break this problem into two subproblems by setting (x + 1.102040817) equal to 3.379138291 and -3.379138291.Subproblem 1
x + 1.102040817 = 3.379138291 Simplifying x + 1.102040817 = 3.379138291 Reorder the terms: 1.102040817 + x = 3.379138291 Solving 1.102040817 + x = 3.379138291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.102040817' to each side of the equation. 1.102040817 + -1.102040817 + x = 3.379138291 + -1.102040817 Combine like terms: 1.102040817 + -1.102040817 = 0.000000000 0.000000000 + x = 3.379138291 + -1.102040817 x = 3.379138291 + -1.102040817 Combine like terms: 3.379138291 + -1.102040817 = 2.277097474 x = 2.277097474 Simplifying x = 2.277097474Subproblem 2
x + 1.102040817 = -3.379138291 Simplifying x + 1.102040817 = -3.379138291 Reorder the terms: 1.102040817 + x = -3.379138291 Solving 1.102040817 + x = -3.379138291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.102040817' to each side of the equation. 1.102040817 + -1.102040817 + x = -3.379138291 + -1.102040817 Combine like terms: 1.102040817 + -1.102040817 = 0.000000000 0.000000000 + x = -3.379138291 + -1.102040817 x = -3.379138291 + -1.102040817 Combine like terms: -3.379138291 + -1.102040817 = -4.481179108 x = -4.481179108 Simplifying x = -4.481179108Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.277097474, -4.481179108}
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