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Simplifying -78 = -10.8x + -4.9x2 Solving -78 = -10.8x + -4.9x2 Solving for variable 'x'. Reorder the terms: -78 + 10.8x + 4.9x2 = -10.8x + 10.8x + -4.9x2 + 4.9x2 Combine like terms: -10.8x + 10.8x = 0.0 -78 + 10.8x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -78 + 10.8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -78 + 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'. -15.91836735 + 2.204081633x + x2 = 0 Move the constant term to the right: Add '15.91836735' to each side of the equation. -15.91836735 + 2.204081633x + 15.91836735 + x2 = 0 + 15.91836735 Reorder the terms: -15.91836735 + 15.91836735 + 2.204081633x + x2 = 0 + 15.91836735 Combine like terms: -15.91836735 + 15.91836735 = 0.00000000 0.00000000 + 2.204081633x + x2 = 0 + 15.91836735 2.204081633x + x2 = 0 + 15.91836735 Combine like terms: 0 + 15.91836735 = 15.91836735 2.204081633x + x2 = 15.91836735 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 = 15.91836735 + 1.214493962 Reorder the terms: 1.214493962 + 2.204081633x + x2 = 15.91836735 + 1.214493962 Combine like terms: 15.91836735 + 1.214493962 = 17.132861312 1.214493962 + 2.204081633x + x2 = 17.132861312 Factor a perfect square on the left side: (x + 1.102040817)(x + 1.102040817) = 17.132861312 Calculate the square root of the right side: 4.139186069 Break this problem into two subproblems by setting (x + 1.102040817) equal to 4.139186069 and -4.139186069.Subproblem 1
x + 1.102040817 = 4.139186069 Simplifying x + 1.102040817 = 4.139186069 Reorder the terms: 1.102040817 + x = 4.139186069 Solving 1.102040817 + x = 4.139186069 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 = 4.139186069 + -1.102040817 Combine like terms: 1.102040817 + -1.102040817 = 0.000000000 0.000000000 + x = 4.139186069 + -1.102040817 x = 4.139186069 + -1.102040817 Combine like terms: 4.139186069 + -1.102040817 = 3.037145252 x = 3.037145252 Simplifying x = 3.037145252Subproblem 2
x + 1.102040817 = -4.139186069 Simplifying x + 1.102040817 = -4.139186069 Reorder the terms: 1.102040817 + x = -4.139186069 Solving 1.102040817 + x = -4.139186069 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 = -4.139186069 + -1.102040817 Combine like terms: 1.102040817 + -1.102040817 = 0.000000000 0.000000000 + x = -4.139186069 + -1.102040817 x = -4.139186069 + -1.102040817 Combine like terms: -4.139186069 + -1.102040817 = -5.241226886 x = -5.241226886 Simplifying x = -5.241226886Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.037145252, -5.241226886}
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