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Simplifying 5x2 + -55x + 150 = -30 + 11x Reorder the terms: 150 + -55x + 5x2 = -30 + 11x Solving 150 + -55x + 5x2 = -30 + 11x Solving for variable 'x'. Reorder the terms: 150 + 30 + -55x + -11x + 5x2 = -30 + 11x + 30 + -11x Combine like terms: 150 + 30 = 180 180 + -55x + -11x + 5x2 = -30 + 11x + 30 + -11x Combine like terms: -55x + -11x = -66x 180 + -66x + 5x2 = -30 + 11x + 30 + -11x Reorder the terms: 180 + -66x + 5x2 = -30 + 30 + 11x + -11x Combine like terms: -30 + 30 = 0 180 + -66x + 5x2 = 0 + 11x + -11x 180 + -66x + 5x2 = 11x + -11x Combine like terms: 11x + -11x = 0 180 + -66x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 36 + -13.2x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -13.2x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -13.2x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -13.2x + x2 = 0 + -36 -13.2x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -13.2x + x2 = -36 The x term is -13.2x. Take half its coefficient (-6.6). Square it (43.56) and add it to both sides. Add '43.56' to each side of the equation. -13.2x + 43.56 + x2 = -36 + 43.56 Reorder the terms: 43.56 + -13.2x + x2 = -36 + 43.56 Combine like terms: -36 + 43.56 = 7.56 43.56 + -13.2x + x2 = 7.56 Factor a perfect square on the left side: (x + -6.6)(x + -6.6) = 7.56 Calculate the square root of the right side: 2.749545417 Break this problem into two subproblems by setting (x + -6.6) equal to 2.749545417 and -2.749545417.Subproblem 1
x + -6.6 = 2.749545417 Simplifying x + -6.6 = 2.749545417 Reorder the terms: -6.6 + x = 2.749545417 Solving -6.6 + x = 2.749545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.6' to each side of the equation. -6.6 + 6.6 + x = 2.749545417 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + x = 2.749545417 + 6.6 x = 2.749545417 + 6.6 Combine like terms: 2.749545417 + 6.6 = 9.349545417 x = 9.349545417 Simplifying x = 9.349545417Subproblem 2
x + -6.6 = -2.749545417 Simplifying x + -6.6 = -2.749545417 Reorder the terms: -6.6 + x = -2.749545417 Solving -6.6 + x = -2.749545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.6' to each side of the equation. -6.6 + 6.6 + x = -2.749545417 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + x = -2.749545417 + 6.6 x = -2.749545417 + 6.6 Combine like terms: -2.749545417 + 6.6 = 3.850454583 x = 3.850454583 Simplifying x = 3.850454583Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.349545417, 3.850454583}
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