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Simplifying x(5x + -23) = 26 Reorder the terms: x(-23 + 5x) = 26 (-23 * x + 5x * x) = 26 (-23x + 5x2) = 26 Solving -23x + 5x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -23x + 5x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -23x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.2 + -4.6x + x2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + -4.6x + 5.2 + x2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + -4.6x + x2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + -4.6x + x2 = 0 + 5.2 -4.6x + x2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 -4.6x + x2 = 5.2 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 5.2 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 5.2 + 5.29 Combine like terms: 5.2 + 5.29 = 10.49 5.29 + -4.6x + x2 = 10.49 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 10.49 Calculate the square root of the right side: 3.238826948 Break this problem into two subproblems by setting (x + -2.3) equal to 3.238826948 and -3.238826948.Subproblem 1
x + -2.3 = 3.238826948 Simplifying x + -2.3 = 3.238826948 Reorder the terms: -2.3 + x = 3.238826948 Solving -2.3 + x = 3.238826948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 3.238826948 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 3.238826948 + 2.3 x = 3.238826948 + 2.3 Combine like terms: 3.238826948 + 2.3 = 5.538826948 x = 5.538826948 Simplifying x = 5.538826948Subproblem 2
x + -2.3 = -3.238826948 Simplifying x + -2.3 = -3.238826948 Reorder the terms: -2.3 + x = -3.238826948 Solving -2.3 + x = -3.238826948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -3.238826948 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -3.238826948 + 2.3 x = -3.238826948 + 2.3 Combine like terms: -3.238826948 + 2.3 = -0.938826948 x = -0.938826948 Simplifying x = -0.938826948Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.538826948, -0.938826948}
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