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Simplifying x2 + 23x + 34 = 45 Reorder the terms: 34 + 23x + x2 = 45 Solving 34 + 23x + x2 = 45 Solving for variable 'x'. Reorder the terms: 34 + -45 + 23x + x2 = 45 + -45 Combine like terms: 34 + -45 = -11 -11 + 23x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -11 + 23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 23x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 23x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 23x + x2 = 0 + 11 23x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 23x + x2 = 11 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 11 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 11 + 132.25 Combine like terms: 11 + 132.25 = 143.25 132.25 + 23x + x2 = 143.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 143.25 Calculate the square root of the right side: 11.968709204 Break this problem into two subproblems by setting (x + 11.5) equal to 11.968709204 and -11.968709204.Subproblem 1
x + 11.5 = 11.968709204 Simplifying x + 11.5 = 11.968709204 Reorder the terms: 11.5 + x = 11.968709204 Solving 11.5 + x = 11.968709204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 11.968709204 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 11.968709204 + -11.5 x = 11.968709204 + -11.5 Combine like terms: 11.968709204 + -11.5 = 0.468709204 x = 0.468709204 Simplifying x = 0.468709204Subproblem 2
x + 11.5 = -11.968709204 Simplifying x + 11.5 = -11.968709204 Reorder the terms: 11.5 + x = -11.968709204 Solving 11.5 + x = -11.968709204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -11.968709204 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -11.968709204 + -11.5 x = -11.968709204 + -11.5 Combine like terms: -11.968709204 + -11.5 = -23.468709204 x = -23.468709204 Simplifying x = -23.468709204Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.468709204, -23.468709204}
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