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Simplifying x2 + 55x + -66 = 78 Reorder the terms: -66 + 55x + x2 = 78 Solving -66 + 55x + x2 = 78 Solving for variable 'x'. Reorder the terms: -66 + -78 + 55x + x2 = 78 + -78 Combine like terms: -66 + -78 = -144 -144 + 55x + x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -144 + 55x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 55x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 55x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 55x + x2 = 0 + 144 55x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 55x + x2 = 144 The x term is 55x. Take half its coefficient (27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. 55x + 756.25 + x2 = 144 + 756.25 Reorder the terms: 756.25 + 55x + x2 = 144 + 756.25 Combine like terms: 144 + 756.25 = 900.25 756.25 + 55x + x2 = 900.25 Factor a perfect square on the left side: (x + 27.5)(x + 27.5) = 900.25 Calculate the square root of the right side: 30.004166377 Break this problem into two subproblems by setting (x + 27.5) equal to 30.004166377 and -30.004166377.Subproblem 1
x + 27.5 = 30.004166377 Simplifying x + 27.5 = 30.004166377 Reorder the terms: 27.5 + x = 30.004166377 Solving 27.5 + x = 30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 30.004166377 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 30.004166377 + -27.5 x = 30.004166377 + -27.5 Combine like terms: 30.004166377 + -27.5 = 2.504166377 x = 2.504166377 Simplifying x = 2.504166377Subproblem 2
x + 27.5 = -30.004166377 Simplifying x + 27.5 = -30.004166377 Reorder the terms: 27.5 + x = -30.004166377 Solving 27.5 + x = -30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -30.004166377 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -30.004166377 + -27.5 x = -30.004166377 + -27.5 Combine like terms: -30.004166377 + -27.5 = -57.504166377 x = -57.504166377 Simplifying x = -57.504166377Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.504166377, -57.504166377}
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