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Simplifying 0 = 2x2 + 30x + 87.5 Reorder the terms: 0 = 87.5 + 30x + 2x2 Solving 0 = 87.5 + 30x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -87.5 = -87.5 -87.5 + -30x + -2x2 = 87.5 + 30x + 2x2 + -87.5 + -30x + -2x2 Reorder the terms: -87.5 + -30x + -2x2 = 87.5 + -87.5 + 30x + -30x + 2x2 + -2x2 Combine like terms: 87.5 + -87.5 = 0.0 -87.5 + -30x + -2x2 = 0.0 + 30x + -30x + 2x2 + -2x2 -87.5 + -30x + -2x2 = 30x + -30x + 2x2 + -2x2 Combine like terms: 30x + -30x = 0 -87.5 + -30x + -2x2 = 0 + 2x2 + -2x2 -87.5 + -30x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -87.5 + -30x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 43.75 + 15x + x2 = 0 Move the constant term to the right: Add '-43.75' to each side of the equation. 43.75 + 15x + -43.75 + x2 = 0 + -43.75 Reorder the terms: 43.75 + -43.75 + 15x + x2 = 0 + -43.75 Combine like terms: 43.75 + -43.75 = 0.00 0.00 + 15x + x2 = 0 + -43.75 15x + x2 = 0 + -43.75 Combine like terms: 0 + -43.75 = -43.75 15x + x2 = -43.75 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -43.75 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -43.75 + 56.25 Combine like terms: -43.75 + 56.25 = 12.5 56.25 + 15x + x2 = 12.5 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + 7.5) equal to 3.535533906 and -3.535533906.Subproblem 1
x + 7.5 = 3.535533906 Simplifying x + 7.5 = 3.535533906 Reorder the terms: 7.5 + x = 3.535533906 Solving 7.5 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 3.535533906 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 3.535533906 + -7.5 x = 3.535533906 + -7.5 Combine like terms: 3.535533906 + -7.5 = -3.964466094 x = -3.964466094 Simplifying x = -3.964466094Subproblem 2
x + 7.5 = -3.535533906 Simplifying x + 7.5 = -3.535533906 Reorder the terms: 7.5 + x = -3.535533906 Solving 7.5 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -3.535533906 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -3.535533906 + -7.5 x = -3.535533906 + -7.5 Combine like terms: -3.535533906 + -7.5 = -11.035533906 x = -11.035533906 Simplifying x = -11.035533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.964466094, -11.035533906}
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