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Simplifying 1.25x2 + x + -1155 = 0 Reorder the terms: -1155 + x + 1.25x2 = 0 Solving -1155 + x + 1.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. -924 + 0.8x + x2 = 0 Move the constant term to the right: Add '924' to each side of the equation. -924 + 0.8x + 924 + x2 = 0 + 924 Reorder the terms: -924 + 924 + 0.8x + x2 = 0 + 924 Combine like terms: -924 + 924 = 0 0 + 0.8x + x2 = 0 + 924 0.8x + x2 = 0 + 924 Combine like terms: 0 + 924 = 924 0.8x + x2 = 924 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.8x + 0.25 + x2 = 924 + 0.25 Reorder the terms: 0.25 + 0.8x + x2 = 924 + 0.25 Combine like terms: 924 + 0.25 = 924.25 0.25 + 0.8x + x2 = 924.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 924.25 Calculate the square root of the right side: 30.401480227 Break this problem into two subproblems by setting (x + 0.5) equal to 30.401480227 and -30.401480227.Subproblem 1
x + 0.5 = 30.401480227 Simplifying x + 0.5 = 30.401480227 Reorder the terms: 0.5 + x = 30.401480227 Solving 0.5 + x = 30.401480227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 30.401480227 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 30.401480227 + -0.5 x = 30.401480227 + -0.5 Combine like terms: 30.401480227 + -0.5 = 29.901480227 x = 29.901480227 Simplifying x = 29.901480227Subproblem 2
x + 0.5 = -30.401480227 Simplifying x + 0.5 = -30.401480227 Reorder the terms: 0.5 + x = -30.401480227 Solving 0.5 + x = -30.401480227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -30.401480227 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -30.401480227 + -0.5 x = -30.401480227 + -0.5 Combine like terms: -30.401480227 + -0.5 = -30.901480227 x = -30.901480227 Simplifying x = -30.901480227Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.901480227, -30.901480227}
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