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Simplifying 23 + x(x + 123 * 15 + -3) = 24x Multiply 123 * 15 23 + x(x + 1845 + -3) = 24x Reorder the terms: 23 + x(1845 + -3 + x) = 24x Combine like terms: 1845 + -3 = 1842 23 + x(1842 + x) = 24x 23 + (1842 * x + x * x) = 24x 23 + (1842x + x2) = 24x Solving 23 + 1842x + x2 = 24x Solving for variable 'x'. Reorder the terms: 23 + 1842x + -24x + x2 = 24x + -24x Combine like terms: 1842x + -24x = 1818x 23 + 1818x + x2 = 24x + -24x Combine like terms: 24x + -24x = 0 23 + 1818x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + 1818x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + 1818x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 1818x + x2 = 0 + -23 1818x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 1818x + x2 = -23 The x term is 1818x. Take half its coefficient (909). Square it (826281) and add it to both sides. Add '826281' to each side of the equation. 1818x + 826281 + x2 = -23 + 826281 Reorder the terms: 826281 + 1818x + x2 = -23 + 826281 Combine like terms: -23 + 826281 = 826258 826281 + 1818x + x2 = 826258 Factor a perfect square on the left side: (x + 909)(x + 909) = 826258 Calculate the square root of the right side: 908.987348647 Break this problem into two subproblems by setting (x + 909) equal to 908.987348647 and -908.987348647.Subproblem 1
x + 909 = 908.987348647 Simplifying x + 909 = 908.987348647 Reorder the terms: 909 + x = 908.987348647 Solving 909 + x = 908.987348647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-909' to each side of the equation. 909 + -909 + x = 908.987348647 + -909 Combine like terms: 909 + -909 = 0 0 + x = 908.987348647 + -909 x = 908.987348647 + -909 Combine like terms: 908.987348647 + -909 = -0.012651353 x = -0.012651353 Simplifying x = -0.012651353Subproblem 2
x + 909 = -908.987348647 Simplifying x + 909 = -908.987348647 Reorder the terms: 909 + x = -908.987348647 Solving 909 + x = -908.987348647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-909' to each side of the equation. 909 + -909 + x = -908.987348647 + -909 Combine like terms: 909 + -909 = 0 0 + x = -908.987348647 + -909 x = -908.987348647 + -909 Combine like terms: -908.987348647 + -909 = -1817.987348647 x = -1817.987348647 Simplifying x = -1817.987348647Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.012651353, -1817.987348647}
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