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Simplifying -26x2 + 52x = -503 Reorder the terms: 52x + -26x2 = -503 Solving 52x + -26x2 = -503 Solving for variable 'x'. Reorder the terms: 503 + 52x + -26x2 = -503 + 503 Combine like terms: -503 + 503 = 0 503 + 52x + -26x2 = 0 Begin completing the square. Divide all terms by -26 the coefficient of the squared term: Divide each side by '-26'. -19.34615385 + -2x + x2 = 0 Move the constant term to the right: Add '19.34615385' to each side of the equation. -19.34615385 + -2x + 19.34615385 + x2 = 0 + 19.34615385 Reorder the terms: -19.34615385 + 19.34615385 + -2x + x2 = 0 + 19.34615385 Combine like terms: -19.34615385 + 19.34615385 = 0.00000000 0.00000000 + -2x + x2 = 0 + 19.34615385 -2x + x2 = 0 + 19.34615385 Combine like terms: 0 + 19.34615385 = 19.34615385 -2x + x2 = 19.34615385 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 19.34615385 + 1 Reorder the terms: 1 + -2x + x2 = 19.34615385 + 1 Combine like terms: 19.34615385 + 1 = 20.34615385 1 + -2x + x2 = 20.34615385 Factor a perfect square on the left side: (x + -1)(x + -1) = 20.34615385 Calculate the square root of the right side: 4.510671109 Break this problem into two subproblems by setting (x + -1) equal to 4.510671109 and -4.510671109.Subproblem 1
x + -1 = 4.510671109 Simplifying x + -1 = 4.510671109 Reorder the terms: -1 + x = 4.510671109 Solving -1 + x = 4.510671109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.510671109 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.510671109 + 1 x = 4.510671109 + 1 Combine like terms: 4.510671109 + 1 = 5.510671109 x = 5.510671109 Simplifying x = 5.510671109Subproblem 2
x + -1 = -4.510671109 Simplifying x + -1 = -4.510671109 Reorder the terms: -1 + x = -4.510671109 Solving -1 + x = -4.510671109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.510671109 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.510671109 + 1 x = -4.510671109 + 1 Combine like terms: -4.510671109 + 1 = -3.510671109 x = -3.510671109 Simplifying x = -3.510671109Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.510671109, -3.510671109}
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