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Simplifying -2x2 + 120x + -788 = 0 Reorder the terms: -788 + 120x + -2x2 = 0 Solving -788 + 120x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-394 + 60x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-394 + 60x + -1x2)' equal to zero and attempt to solve: Simplifying -394 + 60x + -1x2 = 0 Solving -394 + 60x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 394 + -60x + x2 = 0 Move the constant term to the right: Add '-394' to each side of the equation. 394 + -60x + -394 + x2 = 0 + -394 Reorder the terms: 394 + -394 + -60x + x2 = 0 + -394 Combine like terms: 394 + -394 = 0 0 + -60x + x2 = 0 + -394 -60x + x2 = 0 + -394 Combine like terms: 0 + -394 = -394 -60x + x2 = -394 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -394 + 900 Reorder the terms: 900 + -60x + x2 = -394 + 900 Combine like terms: -394 + 900 = 506 900 + -60x + x2 = 506 Factor a perfect square on the left side: (x + -30)(x + -30) = 506 Calculate the square root of the right side: 22.494443758 Break this problem into two subproblems by setting (x + -30) equal to 22.494443758 and -22.494443758.Subproblem 1
x + -30 = 22.494443758 Simplifying x + -30 = 22.494443758 Reorder the terms: -30 + x = 22.494443758 Solving -30 + x = 22.494443758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 22.494443758 + 30 Combine like terms: -30 + 30 = 0 0 + x = 22.494443758 + 30 x = 22.494443758 + 30 Combine like terms: 22.494443758 + 30 = 52.494443758 x = 52.494443758 Simplifying x = 52.494443758Subproblem 2
x + -30 = -22.494443758 Simplifying x + -30 = -22.494443758 Reorder the terms: -30 + x = -22.494443758 Solving -30 + x = -22.494443758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -22.494443758 + 30 Combine like terms: -30 + 30 = 0 0 + x = -22.494443758 + 30 x = -22.494443758 + 30 Combine like terms: -22.494443758 + 30 = 7.505556242 x = 7.505556242 Simplifying x = 7.505556242Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.494443758, 7.505556242}Solution
x = {52.494443758, 7.505556242}
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