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Simplifying (2x + 6)(5x + -2) = (13x + 14) Reorder the terms: (6 + 2x)(5x + -2) = (13x + 14) Reorder the terms: (6 + 2x)(-2 + 5x) = (13x + 14) Multiply (6 + 2x) * (-2 + 5x) (6(-2 + 5x) + 2x * (-2 + 5x)) = (13x + 14) ((-2 * 6 + 5x * 6) + 2x * (-2 + 5x)) = (13x + 14) ((-12 + 30x) + 2x * (-2 + 5x)) = (13x + 14) (-12 + 30x + (-2 * 2x + 5x * 2x)) = (13x + 14) (-12 + 30x + (-4x + 10x2)) = (13x + 14) Combine like terms: 30x + -4x = 26x (-12 + 26x + 10x2) = (13x + 14) Reorder the terms: -12 + 26x + 10x2 = (14 + 13x) Remove parenthesis around (14 + 13x) -12 + 26x + 10x2 = 14 + 13x Solving -12 + 26x + 10x2 = 14 + 13x Solving for variable 'x'. Reorder the terms: -12 + -14 + 26x + -13x + 10x2 = 14 + 13x + -14 + -13x Combine like terms: -12 + -14 = -26 -26 + 26x + -13x + 10x2 = 14 + 13x + -14 + -13x Combine like terms: 26x + -13x = 13x -26 + 13x + 10x2 = 14 + 13x + -14 + -13x Reorder the terms: -26 + 13x + 10x2 = 14 + -14 + 13x + -13x Combine like terms: 14 + -14 = 0 -26 + 13x + 10x2 = 0 + 13x + -13x -26 + 13x + 10x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -26 + 13x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.6 + 1.3x + x2 = 0.0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 1.3x + 2.6 + x2 = 0.0 + 2.6 Reorder the terms: -2.6 + 2.6 + 1.3x + x2 = 0.0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 1.3x + x2 = 0.0 + 2.6 1.3x + x2 = 0.0 + 2.6 Combine like terms: 0.0 + 2.6 = 2.6 1.3x + x2 = 2.6 The x term is 1.3x. Take half its coefficient (0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. 1.3x + 0.4225 + x2 = 2.6 + 0.4225 Reorder the terms: 0.4225 + 1.3x + x2 = 2.6 + 0.4225 Combine like terms: 2.6 + 0.4225 = 3.0225 0.4225 + 1.3x + x2 = 3.0225 Factor a perfect square on the left side: (x + 0.65)(x + 0.65) = 3.0225 Calculate the square root of the right side: 1.738533865 Break this problem into two subproblems by setting (x + 0.65) equal to 1.738533865 and -1.738533865.Subproblem 1
x + 0.65 = 1.738533865 Simplifying x + 0.65 = 1.738533865 Reorder the terms: 0.65 + x = 1.738533865 Solving 0.65 + x = 1.738533865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = 1.738533865 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = 1.738533865 + -0.65 x = 1.738533865 + -0.65 Combine like terms: 1.738533865 + -0.65 = 1.088533865 x = 1.088533865 Simplifying x = 1.088533865Subproblem 2
x + 0.65 = -1.738533865 Simplifying x + 0.65 = -1.738533865 Reorder the terms: 0.65 + x = -1.738533865 Solving 0.65 + x = -1.738533865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = -1.738533865 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = -1.738533865 + -0.65 x = -1.738533865 + -0.65 Combine like terms: -1.738533865 + -0.65 = -2.388533865 x = -2.388533865 Simplifying x = -2.388533865Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.088533865, -2.388533865}
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