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Simplifying (2x + -3)(x + -4) = 21 Reorder the terms: (-3 + 2x)(x + -4) = 21 Reorder the terms: (-3 + 2x)(-4 + x) = 21 Multiply (-3 + 2x) * (-4 + x) (-3(-4 + x) + 2x * (-4 + x)) = 21 ((-4 * -3 + x * -3) + 2x * (-4 + x)) = 21 ((12 + -3x) + 2x * (-4 + x)) = 21 (12 + -3x + (-4 * 2x + x * 2x)) = 21 (12 + -3x + (-8x + 2x2)) = 21 Combine like terms: -3x + -8x = -11x (12 + -11x + 2x2) = 21 Solving 12 + -11x + 2x2 = 21 Solving for variable 'x'. Reorder the terms: 12 + -21 + -11x + 2x2 = 21 + -21 Combine like terms: 12 + -21 = -9 -9 + -11x + 2x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -9 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -5.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -5.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -5.5x + x2 = 0 + 4.5 -5.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -5.5x + x2 = 4.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 4.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 4.5 + 7.5625 Combine like terms: 4.5 + 7.5625 = 12.0625 7.5625 + -5.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + -2.75) equal to 3.473110997 and -3.473110997.Subproblem 1
x + -2.75 = 3.473110997 Simplifying x + -2.75 = 3.473110997 Reorder the terms: -2.75 + x = 3.473110997 Solving -2.75 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.473110997 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.473110997 + 2.75 x = 3.473110997 + 2.75 Combine like terms: 3.473110997 + 2.75 = 6.223110997 x = 6.223110997 Simplifying x = 6.223110997Subproblem 2
x + -2.75 = -3.473110997 Simplifying x + -2.75 = -3.473110997 Reorder the terms: -2.75 + x = -3.473110997 Solving -2.75 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.473110997 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.473110997 + 2.75 x = -3.473110997 + 2.75 Combine like terms: -3.473110997 + 2.75 = -0.723110997 x = -0.723110997 Simplifying x = -0.723110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.223110997, -0.723110997}
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