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Simplifying x2 + -118.75 = -3x Reorder the terms: -118.75 + x2 = -3x Solving -118.75 + x2 = -3x Solving for variable 'x'. Reorder the terms: -118.75 + 3x + x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -118.75 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '118.75' to each side of the equation. -118.75 + 3x + 118.75 + x2 = 0 + 118.75 Reorder the terms: -118.75 + 118.75 + 3x + x2 = 0 + 118.75 Combine like terms: -118.75 + 118.75 = 0.00 0.00 + 3x + x2 = 0 + 118.75 3x + x2 = 0 + 118.75 Combine like terms: 0 + 118.75 = 118.75 3x + x2 = 118.75 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 118.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 118.75 + 2.25 Combine like terms: 118.75 + 2.25 = 121 2.25 + 3x + x2 = 121 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 121 Calculate the square root of the right side: 11 Break this problem into two subproblems by setting (x + 1.5) equal to 11 and -11.Subproblem 1
x + 1.5 = 11 Simplifying x + 1.5 = 11 Reorder the terms: 1.5 + x = 11 Solving 1.5 + x = 11 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 11 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11 + -1.5 x = 11 + -1.5 Combine like terms: 11 + -1.5 = 9.5 x = 9.5 Simplifying x = 9.5Subproblem 2
x + 1.5 = -11 Simplifying x + 1.5 = -11 Reorder the terms: 1.5 + x = -11 Solving 1.5 + x = -11 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -11 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11 + -1.5 x = -11 + -1.5 Combine like terms: -11 + -1.5 = -12.5 x = -12.5 Simplifying x = -12.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.5, -12.5}
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