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Simplifying 0 = 93.5 + -78x + 15x2 Solving 0 = 93.5 + -78x + 15x2 Solving for variable 'x'. Combine like terms: 0 + -93.5 = -93.5 -93.5 + 78x + -15x2 = 93.5 + -78x + 15x2 + -93.5 + 78x + -15x2 Reorder the terms: -93.5 + 78x + -15x2 = 93.5 + -93.5 + -78x + 78x + 15x2 + -15x2 Combine like terms: 93.5 + -93.5 = 0.0 -93.5 + 78x + -15x2 = 0.0 + -78x + 78x + 15x2 + -15x2 -93.5 + 78x + -15x2 = -78x + 78x + 15x2 + -15x2 Combine like terms: -78x + 78x = 0 -93.5 + 78x + -15x2 = 0 + 15x2 + -15x2 -93.5 + 78x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -93.5 + 78x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. 6.233333333 + -5.2x + x2 = 0 Move the constant term to the right: Add '-6.233333333' to each side of the equation. 6.233333333 + -5.2x + -6.233333333 + x2 = 0 + -6.233333333 Reorder the terms: 6.233333333 + -6.233333333 + -5.2x + x2 = 0 + -6.233333333 Combine like terms: 6.233333333 + -6.233333333 = 0.000000000 0.000000000 + -5.2x + x2 = 0 + -6.233333333 -5.2x + x2 = 0 + -6.233333333 Combine like terms: 0 + -6.233333333 = -6.233333333 -5.2x + x2 = -6.233333333 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = -6.233333333 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = -6.233333333 + 6.76 Combine like terms: -6.233333333 + 6.76 = 0.526666667 6.76 + -5.2x + x2 = 0.526666667 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 0.526666667 Calculate the square root of the right side: 0.725718035 Break this problem into two subproblems by setting (x + -2.6) equal to 0.725718035 and -0.725718035.Subproblem 1
x + -2.6 = 0.725718035 Simplifying x + -2.6 = 0.725718035 Reorder the terms: -2.6 + x = 0.725718035 Solving -2.6 + x = 0.725718035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 0.725718035 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 0.725718035 + 2.6 x = 0.725718035 + 2.6 Combine like terms: 0.725718035 + 2.6 = 3.325718035 x = 3.325718035 Simplifying x = 3.325718035Subproblem 2
x + -2.6 = -0.725718035 Simplifying x + -2.6 = -0.725718035 Reorder the terms: -2.6 + x = -0.725718035 Solving -2.6 + x = -0.725718035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -0.725718035 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -0.725718035 + 2.6 x = -0.725718035 + 2.6 Combine like terms: -0.725718035 + 2.6 = 1.874281965 x = 1.874281965 Simplifying x = 1.874281965Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.325718035, 1.874281965}
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