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Simplifying (2x + -1)(x + 5) = 10 Reorder the terms: (-1 + 2x)(x + 5) = 10 Reorder the terms: (-1 + 2x)(5 + x) = 10 Multiply (-1 + 2x) * (5 + x) (-1(5 + x) + 2x * (5 + x)) = 10 ((5 * -1 + x * -1) + 2x * (5 + x)) = 10 ((-5 + -1x) + 2x * (5 + x)) = 10 (-5 + -1x + (5 * 2x + x * 2x)) = 10 (-5 + -1x + (10x + 2x2)) = 10 Combine like terms: -1x + 10x = 9x (-5 + 9x + 2x2) = 10 Solving -5 + 9x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -5 + -10 + 9x + 2x2 = 10 + -10 Combine like terms: -5 + -10 = -15 -15 + 9x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -15 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 4.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 4.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 4.5x + x2 = 0 + 7.5 4.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 4.5x + x2 = 7.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 7.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 7.5 + 5.0625 Combine like terms: 7.5 + 5.0625 = 12.5625 5.0625 + 4.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 2.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 2.25 = 3.54436172 Simplifying x + 2.25 = 3.54436172 Reorder the terms: 2.25 + x = 3.54436172 Solving 2.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.54436172 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.54436172 + -2.25 x = 3.54436172 + -2.25 Combine like terms: 3.54436172 + -2.25 = 1.29436172 x = 1.29436172 Simplifying x = 1.29436172Subproblem 2
x + 2.25 = -3.54436172 Simplifying x + 2.25 = -3.54436172 Reorder the terms: 2.25 + x = -3.54436172 Solving 2.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.54436172 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.54436172 + -2.25 x = -3.54436172 + -2.25 Combine like terms: -3.54436172 + -2.25 = -5.79436172 x = -5.79436172 Simplifying x = -5.79436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.29436172, -5.79436172}
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