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Simplifying -2x2 + 24x + -15 = 0 Reorder the terms: -15 + 24x + -2x2 = 0 Solving -15 + 24x + -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'. 7.5 + -12x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -12x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -12x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -12x + x2 = 0 + -7.5 -12x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -12x + x2 = -7.5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -7.5 + 36 Reorder the terms: 36 + -12x + x2 = -7.5 + 36 Combine like terms: -7.5 + 36 = 28.5 36 + -12x + x2 = 28.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting (x + -6) equal to 5.338539126 and -5.338539126.Subproblem 1
x + -6 = 5.338539126 Simplifying x + -6 = 5.338539126 Reorder the terms: -6 + x = 5.338539126 Solving -6 + x = 5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.338539126 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.338539126 + 6 x = 5.338539126 + 6 Combine like terms: 5.338539126 + 6 = 11.338539126 x = 11.338539126 Simplifying x = 11.338539126Subproblem 2
x + -6 = -5.338539126 Simplifying x + -6 = -5.338539126 Reorder the terms: -6 + x = -5.338539126 Solving -6 + x = -5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.338539126 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.338539126 + 6 x = -5.338539126 + 6 Combine like terms: -5.338539126 + 6 = 0.661460874 x = 0.661460874 Simplifying x = 0.661460874Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.338539126, 0.661460874}
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