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Simplifying -0.06x2 + 1.32x + 30.24 = 0 Reorder the terms: 30.24 + 1.32x + -0.06x2 = 0 Solving 30.24 + 1.32x + -0.06x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. -504 + -22x + x2 = 0 Move the constant term to the right: Add '504' to each side of the equation. -504 + -22x + 504 + x2 = 0 + 504 Reorder the terms: -504 + 504 + -22x + x2 = 0 + 504 Combine like terms: -504 + 504 = 0 0 + -22x + x2 = 0 + 504 -22x + x2 = 0 + 504 Combine like terms: 0 + 504 = 504 -22x + x2 = 504 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = 504 + 121 Reorder the terms: 121 + -22x + x2 = 504 + 121 Combine like terms: 504 + 121 = 625 121 + -22x + x2 = 625 Factor a perfect square on the left side: (x + -11)(x + -11) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + -11) equal to 25 and -25.Subproblem 1
x + -11 = 25 Simplifying x + -11 = 25 Reorder the terms: -11 + x = 25 Solving -11 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 25 + 11 Combine like terms: -11 + 11 = 0 0 + x = 25 + 11 x = 25 + 11 Combine like terms: 25 + 11 = 36 x = 36 Simplifying x = 36Subproblem 2
x + -11 = -25 Simplifying x + -11 = -25 Reorder the terms: -11 + x = -25 Solving -11 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -25 + 11 Combine like terms: -11 + 11 = 0 0 + x = -25 + 11 x = -25 + 11 Combine like terms: -25 + 11 = -14 x = -14 Simplifying x = -14Solution
The solution to the problem is based on the solutions from the subproblems. x = {36, -14}
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