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Simplifying (5x + 4)(x + -20) = 62 + -1(x + -2) Reorder the terms: (4 + 5x)(x + -20) = 62 + -1(x + -2) Reorder the terms: (4 + 5x)(-20 + x) = 62 + -1(x + -2) Multiply (4 + 5x) * (-20 + x) (4(-20 + x) + 5x * (-20 + x)) = 62 + -1(x + -2) ((-20 * 4 + x * 4) + 5x * (-20 + x)) = 62 + -1(x + -2) ((-80 + 4x) + 5x * (-20 + x)) = 62 + -1(x + -2) (-80 + 4x + (-20 * 5x + x * 5x)) = 62 + -1(x + -2) (-80 + 4x + (-100x + 5x2)) = 62 + -1(x + -2) Combine like terms: 4x + -100x = -96x (-80 + -96x + 5x2) = 62 + -1(x + -2) Reorder the terms: -80 + -96x + 5x2 = 62 + -1(-2 + x) -80 + -96x + 5x2 = 62 + (-2 * -1 + x * -1) -80 + -96x + 5x2 = 62 + (2 + -1x) Combine like terms: 62 + 2 = 64 -80 + -96x + 5x2 = 64 + -1x Solving -80 + -96x + 5x2 = 64 + -1x Solving for variable 'x'. Reorder the terms: -80 + -64 + -96x + x + 5x2 = 64 + -1x + -64 + x Combine like terms: -80 + -64 = -144 -144 + -96x + x + 5x2 = 64 + -1x + -64 + x Combine like terms: -96x + x = -95x -144 + -95x + 5x2 = 64 + -1x + -64 + x Reorder the terms: -144 + -95x + 5x2 = 64 + -64 + -1x + x Combine like terms: 64 + -64 = 0 -144 + -95x + 5x2 = 0 + -1x + x -144 + -95x + 5x2 = -1x + x Combine like terms: -1x + x = 0 -144 + -95x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -28.8 + -19x + x2 = 0 Move the constant term to the right: Add '28.8' to each side of the equation. -28.8 + -19x + 28.8 + x2 = 0 + 28.8 Reorder the terms: -28.8 + 28.8 + -19x + x2 = 0 + 28.8 Combine like terms: -28.8 + 28.8 = 0.0 0.0 + -19x + x2 = 0 + 28.8 -19x + x2 = 0 + 28.8 Combine like terms: 0 + 28.8 = 28.8 -19x + x2 = 28.8 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 28.8 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 28.8 + 90.25 Combine like terms: 28.8 + 90.25 = 119.05 90.25 + -19x + x2 = 119.05 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 119.05 Calculate the square root of the right side: 10.91100362 Break this problem into two subproblems by setting (x + -9.5) equal to 10.91100362 and -10.91100362.Subproblem 1
x + -9.5 = 10.91100362 Simplifying x + -9.5 = 10.91100362 Reorder the terms: -9.5 + x = 10.91100362 Solving -9.5 + x = 10.91100362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 10.91100362 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 10.91100362 + 9.5 x = 10.91100362 + 9.5 Combine like terms: 10.91100362 + 9.5 = 20.41100362 x = 20.41100362 Simplifying x = 20.41100362Subproblem 2
x + -9.5 = -10.91100362 Simplifying x + -9.5 = -10.91100362 Reorder the terms: -9.5 + x = -10.91100362 Solving -9.5 + x = -10.91100362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -10.91100362 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -10.91100362 + 9.5 x = -10.91100362 + 9.5 Combine like terms: -10.91100362 + 9.5 = -1.41100362 x = -1.41100362 Simplifying x = -1.41100362Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.41100362, -1.41100362}
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