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Simplifying x2 + 15x + 56.25 = 1 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 1 + 56.25 Combine like terms: 1 + 56.25 = 57.25 56.25 + 15x + x2 = 57.25 Solving 56.25 + 15x + x2 = 57.25 Solving for variable 'x'. Reorder the terms: 56.25 + -57.25 + 15x + x2 = 57.25 + -57.25 Combine like terms: 56.25 + -57.25 = -1 -1 + 15x + x2 = 57.25 + -57.25 Combine like terms: 57.25 + -57.25 = 0.00 -1 + 15x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 15x + 1 + x2 = 0.00 + 1 Reorder the terms: -1 + 1 + 15x + x2 = 0.00 + 1 Combine like terms: -1 + 1 = 0 0 + 15x + x2 = 0.00 + 1 15x + x2 = 0.00 + 1 Combine like terms: 0.00 + 1 = 1 15x + x2 = 1 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 = 1 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 1 + 56.25 Combine like terms: 1 + 56.25 = 57.25 56.25 + 15x + x2 = 57.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + 7.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + 7.5 = 7.566372975 Simplifying x + 7.5 = 7.566372975 Reorder the terms: 7.5 + x = 7.566372975 Solving 7.5 + x = 7.566372975 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 = 7.566372975 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.566372975 + -7.5 x = 7.566372975 + -7.5 Combine like terms: 7.566372975 + -7.5 = 0.066372975 x = 0.066372975 Simplifying x = 0.066372975Subproblem 2
x + 7.5 = -7.566372975 Simplifying x + 7.5 = -7.566372975 Reorder the terms: 7.5 + x = -7.566372975 Solving 7.5 + x = -7.566372975 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 = -7.566372975 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.566372975 + -7.5 x = -7.566372975 + -7.5 Combine like terms: -7.566372975 + -7.5 = -15.066372975 x = -15.066372975 Simplifying x = -15.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.066372975, -15.066372975}
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