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Simplifying (x + 5)(2x + -6) = x Reorder the terms: (5 + x)(2x + -6) = x Reorder the terms: (5 + x)(-6 + 2x) = x Multiply (5 + x) * (-6 + 2x) (5(-6 + 2x) + x(-6 + 2x)) = x ((-6 * 5 + 2x * 5) + x(-6 + 2x)) = x ((-30 + 10x) + x(-6 + 2x)) = x (-30 + 10x + (-6 * x + 2x * x)) = x (-30 + 10x + (-6x + 2x2)) = x Combine like terms: 10x + -6x = 4x (-30 + 4x + 2x2) = x Solving -30 + 4x + 2x2 = x Solving for variable 'x'. Reorder the terms: -30 + 4x + -1x + 2x2 = x + -1x Combine like terms: 4x + -1x = 3x -30 + 3x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -30 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15 + 1.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 1.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 1.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 1.5x + x2 = 0 + 15 1.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 1.5x + x2 = 15 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 15 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 15 + 0.5625 Combine like terms: 15 + 0.5625 = 15.5625 0.5625 + 1.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + 0.75) equal to 3.94493346 and -3.94493346.Subproblem 1
x + 0.75 = 3.94493346 Simplifying x + 0.75 = 3.94493346 Reorder the terms: 0.75 + x = 3.94493346 Solving 0.75 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 3.94493346 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.94493346 + -0.75 x = 3.94493346 + -0.75 Combine like terms: 3.94493346 + -0.75 = 3.19493346 x = 3.19493346 Simplifying x = 3.19493346Subproblem 2
x + 0.75 = -3.94493346 Simplifying x + 0.75 = -3.94493346 Reorder the terms: 0.75 + x = -3.94493346 Solving 0.75 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -3.94493346 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.94493346 + -0.75 x = -3.94493346 + -0.75 Combine like terms: -3.94493346 + -0.75 = -4.69493346 x = -4.69493346 Simplifying x = -4.69493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.19493346, -4.69493346}
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