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Simplifying x2 + 15x + 56.25 = 0 Reorder the terms: 56.25 + 15x + x2 = 0 Solving 56.25 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-56.25' to each side of the equation. 56.25 + 15x + -56.25 + x2 = 0 + -56.25 Reorder the terms: 56.25 + -56.25 + 15x + x2 = 0 + -56.25 Combine like terms: 56.25 + -56.25 = 0.00 0.00 + 15x + x2 = 0 + -56.25 15x + x2 = 0 + -56.25 Combine like terms: 0 + -56.25 = -56.25 15x + x2 = -56.25 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 = -56.25 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -56.25 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 56.25 + 15x + x2 = 0.00 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 7.5) equal to 0.00 and 0.00.Subproblem 1
x + 7.5 = 0.00 Simplifying x + 7.5 = 0.00 Reorder the terms: 7.5 + x = 0.00 Solving 7.5 + x = 0.00 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 = 0.00 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 0.00 + -7.5 x = 0.00 + -7.5 Combine like terms: 0.00 + -7.5 = -7.5 x = -7.5 Simplifying x = -7.5Subproblem 2
x + 7.5 = 0.00 Simplifying x + 7.5 = 0.00 Reorder the terms: 7.5 + x = 0.00 Solving 7.5 + x = 0.00 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 = 0.00 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 0.00 + -7.5 x = 0.00 + -7.5 Combine like terms: 0.00 + -7.5 = -7.5 x = -7.5 Simplifying x = -7.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.5, -7.5}
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