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Simplifying 2x2 + -3x + -118 = 0 Reorder the terms: -118 + -3x + 2x2 = 0 Solving -118 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -59 + -1.5x + x2 = 0 Move the constant term to the right: Add '59' to each side of the equation. -59 + -1.5x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + -1.5x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + -1.5x + x2 = 0 + 59 -1.5x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 -1.5x + x2 = 59 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 59 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 59 + 0.5625 Combine like terms: 59 + 0.5625 = 59.5625 0.5625 + -1.5x + x2 = 59.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 59.5625 Calculate the square root of the right side: 7.71767452 Break this problem into two subproblems by setting (x + -0.75) equal to 7.71767452 and -7.71767452.Subproblem 1
x + -0.75 = 7.71767452 Simplifying x + -0.75 = 7.71767452 Reorder the terms: -0.75 + x = 7.71767452 Solving -0.75 + x = 7.71767452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 7.71767452 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 7.71767452 + 0.75 x = 7.71767452 + 0.75 Combine like terms: 7.71767452 + 0.75 = 8.46767452 x = 8.46767452 Simplifying x = 8.46767452Subproblem 2
x + -0.75 = -7.71767452 Simplifying x + -0.75 = -7.71767452 Reorder the terms: -0.75 + x = -7.71767452 Solving -0.75 + x = -7.71767452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -7.71767452 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -7.71767452 + 0.75 x = -7.71767452 + 0.75 Combine like terms: -7.71767452 + 0.75 = -6.96767452 x = -6.96767452 Simplifying x = -6.96767452Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.46767452, -6.96767452}
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