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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 = 5.79436172 x = 5.79436172 Simplifying x = 5.79436172Subproblem 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 = -1.29436172 x = -1.29436172 Simplifying x = -1.29436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.79436172, -1.29436172}
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