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Simplifying (5x + -8)(5x + -8) = 42 Reorder the terms: (-8 + 5x)(5x + -8) = 42 Reorder the terms: (-8 + 5x)(-8 + 5x) = 42 Multiply (-8 + 5x) * (-8 + 5x) (-8(-8 + 5x) + 5x * (-8 + 5x)) = 42 ((-8 * -8 + 5x * -8) + 5x * (-8 + 5x)) = 42 ((64 + -40x) + 5x * (-8 + 5x)) = 42 (64 + -40x + (-8 * 5x + 5x * 5x)) = 42 (64 + -40x + (-40x + 25x2)) = 42 Combine like terms: -40x + -40x = -80x (64 + -80x + 25x2) = 42 Solving 64 + -80x + 25x2 = 42 Solving for variable 'x'. Reorder the terms: 64 + -42 + -80x + 25x2 = 42 + -42 Combine like terms: 64 + -42 = 22 22 + -80x + 25x2 = 42 + -42 Combine like terms: 42 + -42 = 0 22 + -80x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.88 + -3.2x + x2 = 0 Move the constant term to the right: Add '-0.88' to each side of the equation. 0.88 + -3.2x + -0.88 + x2 = 0 + -0.88 Reorder the terms: 0.88 + -0.88 + -3.2x + x2 = 0 + -0.88 Combine like terms: 0.88 + -0.88 = 0.00 0.00 + -3.2x + x2 = 0 + -0.88 -3.2x + x2 = 0 + -0.88 Combine like terms: 0 + -0.88 = -0.88 -3.2x + x2 = -0.88 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = -0.88 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = -0.88 + 2.56 Combine like terms: -0.88 + 2.56 = 1.68 2.56 + -3.2x + x2 = 1.68 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 1.68 Calculate the square root of the right side: 1.29614814 Break this problem into two subproblems by setting (x + -1.6) equal to 1.29614814 and -1.29614814.Subproblem 1
x + -1.6 = 1.29614814 Simplifying x + -1.6 = 1.29614814 Reorder the terms: -1.6 + x = 1.29614814 Solving -1.6 + x = 1.29614814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 1.29614814 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 1.29614814 + 1.6 x = 1.29614814 + 1.6 Combine like terms: 1.29614814 + 1.6 = 2.89614814 x = 2.89614814 Simplifying x = 2.89614814Subproblem 2
x + -1.6 = -1.29614814 Simplifying x + -1.6 = -1.29614814 Reorder the terms: -1.6 + x = -1.29614814 Solving -1.6 + x = -1.29614814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -1.29614814 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -1.29614814 + 1.6 x = -1.29614814 + 1.6 Combine like terms: -1.29614814 + 1.6 = 0.30385186 x = 0.30385186 Simplifying x = 0.30385186Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.89614814, 0.30385186}
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