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Simplifying x * x + x * x + -10x + 25 = 18 * 18 Multiply x * x x2 + x * x + -10x + 25 = 18 * 18 Multiply x * x x2 + x2 + -10x + 25 = 18 * 18 Reorder the terms: 25 + -10x + x2 + x2 = 18 * 18 Combine like terms: x2 + x2 = 2x2 25 + -10x + 2x2 = 18 * 18 Multiply 18 * 18 25 + -10x + 2x2 = 324 Solving 25 + -10x + 2x2 = 324 Solving for variable 'x'. Reorder the terms: 25 + -324 + -10x + 2x2 = 324 + -324 Combine like terms: 25 + -324 = -299 -299 + -10x + 2x2 = 324 + -324 Combine like terms: 324 + -324 = 0 -299 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -149.5 + -5x + x2 = 0 Move the constant term to the right: Add '149.5' to each side of the equation. -149.5 + -5x + 149.5 + x2 = 0 + 149.5 Reorder the terms: -149.5 + 149.5 + -5x + x2 = 0 + 149.5 Combine like terms: -149.5 + 149.5 = 0.0 0.0 + -5x + x2 = 0 + 149.5 -5x + x2 = 0 + 149.5 Combine like terms: 0 + 149.5 = 149.5 -5x + x2 = 149.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 149.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 149.5 + 6.25 Combine like terms: 149.5 + 6.25 = 155.75 6.25 + -5x + x2 = 155.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 155.75 Calculate the square root of the right side: 12.479983974 Break this problem into two subproblems by setting (x + -2.5) equal to 12.479983974 and -12.479983974.Subproblem 1
x + -2.5 = 12.479983974 Simplifying x + -2.5 = 12.479983974 Reorder the terms: -2.5 + x = 12.479983974 Solving -2.5 + x = 12.479983974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 12.479983974 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 12.479983974 + 2.5 x = 12.479983974 + 2.5 Combine like terms: 12.479983974 + 2.5 = 14.979983974 x = 14.979983974 Simplifying x = 14.979983974Subproblem 2
x + -2.5 = -12.479983974 Simplifying x + -2.5 = -12.479983974 Reorder the terms: -2.5 + x = -12.479983974 Solving -2.5 + x = -12.479983974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -12.479983974 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -12.479983974 + 2.5 x = -12.479983974 + 2.5 Combine like terms: -12.479983974 + 2.5 = -9.979983974 x = -9.979983974 Simplifying x = -9.979983974Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.979983974, -9.979983974}
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