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Simplifying (4x + -1)(x + -2) = 62 Reorder the terms: (-1 + 4x)(x + -2) = 62 Reorder the terms: (-1 + 4x)(-2 + x) = 62 Multiply (-1 + 4x) * (-2 + x) (-1(-2 + x) + 4x * (-2 + x)) = 62 ((-2 * -1 + x * -1) + 4x * (-2 + x)) = 62 ((2 + -1x) + 4x * (-2 + x)) = 62 (2 + -1x + (-2 * 4x + x * 4x)) = 62 (2 + -1x + (-8x + 4x2)) = 62 Combine like terms: -1x + -8x = -9x (2 + -9x + 4x2) = 62 Solving 2 + -9x + 4x2 = 62 Solving for variable 'x'. Reorder the terms: 2 + -62 + -9x + 4x2 = 62 + -62 Combine like terms: 2 + -62 = -60 -60 + -9x + 4x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -60 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15 + -2.25x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -2.25x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -2.25x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2.25x + x2 = 0 + 15 -2.25x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -2.25x + x2 = 15 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 15 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 15 + 1.265625 Combine like terms: 15 + 1.265625 = 16.265625 1.265625 + -2.25x + x2 = 16.265625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 16.265625 Calculate the square root of the right side: 4.033066451 Break this problem into two subproblems by setting (x + -1.125) equal to 4.033066451 and -4.033066451.Subproblem 1
x + -1.125 = 4.033066451 Simplifying x + -1.125 = 4.033066451 Reorder the terms: -1.125 + x = 4.033066451 Solving -1.125 + x = 4.033066451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 4.033066451 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 4.033066451 + 1.125 x = 4.033066451 + 1.125 Combine like terms: 4.033066451 + 1.125 = 5.158066451 x = 5.158066451 Simplifying x = 5.158066451Subproblem 2
x + -1.125 = -4.033066451 Simplifying x + -1.125 = -4.033066451 Reorder the terms: -1.125 + x = -4.033066451 Solving -1.125 + x = -4.033066451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -4.033066451 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -4.033066451 + 1.125 x = -4.033066451 + 1.125 Combine like terms: -4.033066451 + 1.125 = -2.908066451 x = -2.908066451 Simplifying x = -2.908066451Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.158066451, -2.908066451}
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