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Simplifying 2x2 + -4x + -23 = (x + -1) Reorder the terms: -23 + -4x + 2x2 = (x + -1) Reorder the terms: -23 + -4x + 2x2 = (-1 + x) Remove parenthesis around (-1 + x) -23 + -4x + 2x2 = -1 + x Solving -23 + -4x + 2x2 = -1 + x Solving for variable 'x'. Reorder the terms: -23 + 1 + -4x + -1x + 2x2 = -1 + x + 1 + -1x Combine like terms: -23 + 1 = -22 -22 + -4x + -1x + 2x2 = -1 + x + 1 + -1x Combine like terms: -4x + -1x = -5x -22 + -5x + 2x2 = -1 + x + 1 + -1x Reorder the terms: -22 + -5x + 2x2 = -1 + 1 + x + -1x Combine like terms: -1 + 1 = 0 -22 + -5x + 2x2 = 0 + x + -1x -22 + -5x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -22 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11 + -2.5x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -2.5x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -2.5x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2.5x + x2 = 0 + 11 -2.5x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -2.5x + x2 = 11 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 11 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 11 + 1.5625 Combine like terms: 11 + 1.5625 = 12.5625 1.5625 + -2.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + -1.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + -1.25 = 3.54436172 Simplifying x + -1.25 = 3.54436172 Reorder the terms: -1.25 + x = 3.54436172 Solving -1.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.54436172 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.54436172 + 1.25 x = 3.54436172 + 1.25 Combine like terms: 3.54436172 + 1.25 = 4.79436172 x = 4.79436172 Simplifying x = 4.79436172Subproblem 2
x + -1.25 = -3.54436172 Simplifying x + -1.25 = -3.54436172 Reorder the terms: -1.25 + x = -3.54436172 Solving -1.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.54436172 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.54436172 + 1.25 x = -3.54436172 + 1.25 Combine like terms: -3.54436172 + 1.25 = -2.29436172 x = -2.29436172 Simplifying x = -2.29436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.79436172, -2.29436172}
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