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Simplifying 4x2 + -26x + 169 = 142 Reorder the terms: 169 + -26x + 4x2 = 142 Solving 169 + -26x + 4x2 = 142 Solving for variable 'x'. Reorder the terms: 169 + -142 + -26x + 4x2 = 142 + -142 Combine like terms: 169 + -142 = 27 27 + -26x + 4x2 = 142 + -142 Combine like terms: 142 + -142 = 0 27 + -26x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.75 + -6.5x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + -6.5x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + -6.5x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + -6.5x + x2 = 0 + -6.75 -6.5x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 -6.5x + x2 = -6.75 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -6.75 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -6.75 + 10.5625 Combine like terms: -6.75 + 10.5625 = 3.8125 10.5625 + -6.5x + x2 = 3.8125 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (x + -3.25) equal to 1.952562419 and -1.952562419.Subproblem 1
x + -3.25 = 1.952562419 Simplifying x + -3.25 = 1.952562419 Reorder the terms: -3.25 + x = 1.952562419 Solving -3.25 + x = 1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 1.952562419 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 1.952562419 + 3.25 x = 1.952562419 + 3.25 Combine like terms: 1.952562419 + 3.25 = 5.202562419 x = 5.202562419 Simplifying x = 5.202562419Subproblem 2
x + -3.25 = -1.952562419 Simplifying x + -3.25 = -1.952562419 Reorder the terms: -3.25 + x = -1.952562419 Solving -3.25 + x = -1.952562419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -1.952562419 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -1.952562419 + 3.25 x = -1.952562419 + 3.25 Combine like terms: -1.952562419 + 3.25 = 1.297437581 x = 1.297437581 Simplifying x = 1.297437581Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.202562419, 1.297437581}
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