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Simplifying (5x + 2)(2x + -1) = 100 Reorder the terms: (2 + 5x)(2x + -1) = 100 Reorder the terms: (2 + 5x)(-1 + 2x) = 100 Multiply (2 + 5x) * (-1 + 2x) (2(-1 + 2x) + 5x * (-1 + 2x)) = 100 ((-1 * 2 + 2x * 2) + 5x * (-1 + 2x)) = 100 ((-2 + 4x) + 5x * (-1 + 2x)) = 100 (-2 + 4x + (-1 * 5x + 2x * 5x)) = 100 (-2 + 4x + (-5x + 10x2)) = 100 Combine like terms: 4x + -5x = -1x (-2 + -1x + 10x2) = 100 Solving -2 + -1x + 10x2 = 100 Solving for variable 'x'. Reorder the terms: -2 + -100 + -1x + 10x2 = 100 + -100 Combine like terms: -2 + -100 = -102 -102 + -1x + 10x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -102 + -1x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -10.2 + -0.1x + x2 = 0.0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + -0.1x + 10.2 + x2 = 0.0 + 10.2 Reorder the terms: -10.2 + 10.2 + -0.1x + x2 = 0.0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + -0.1x + x2 = 0.0 + 10.2 -0.1x + x2 = 0.0 + 10.2 Combine like terms: 0.0 + 10.2 = 10.2 -0.1x + x2 = 10.2 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 10.2 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 10.2 + 0.0025 Combine like terms: 10.2 + 0.0025 = 10.2025 0.0025 + -0.1x + x2 = 10.2025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 10.2025 Calculate the square root of the right side: 3.194135251 Break this problem into two subproblems by setting (x + -0.05) equal to 3.194135251 and -3.194135251.Subproblem 1
x + -0.05 = 3.194135251 Simplifying x + -0.05 = 3.194135251 Reorder the terms: -0.05 + x = 3.194135251 Solving -0.05 + x = 3.194135251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 3.194135251 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 3.194135251 + 0.05 x = 3.194135251 + 0.05 Combine like terms: 3.194135251 + 0.05 = 3.244135251 x = 3.244135251 Simplifying x = 3.244135251Subproblem 2
x + -0.05 = -3.194135251 Simplifying x + -0.05 = -3.194135251 Reorder the terms: -0.05 + x = -3.194135251 Solving -0.05 + x = -3.194135251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -3.194135251 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -3.194135251 + 0.05 x = -3.194135251 + 0.05 Combine like terms: -3.194135251 + 0.05 = -3.144135251 x = -3.144135251 Simplifying x = -3.144135251Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.244135251, -3.144135251}
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