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Simplifying x2 + 62x + 45 = 0 Reorder the terms: 45 + 62x + x2 = 0 Solving 45 + 62x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 62x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 62x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 62x + x2 = 0 + -45 62x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 62x + x2 = -45 The x term is 62x. Take half its coefficient (31). Square it (961) and add it to both sides. Add '961' to each side of the equation. 62x + 961 + x2 = -45 + 961 Reorder the terms: 961 + 62x + x2 = -45 + 961 Combine like terms: -45 + 961 = 916 961 + 62x + x2 = 916 Factor a perfect square on the left side: (x + 31)(x + 31) = 916 Calculate the square root of the right side: 30.265491901 Break this problem into two subproblems by setting (x + 31) equal to 30.265491901 and -30.265491901.Subproblem 1
x + 31 = 30.265491901 Simplifying x + 31 = 30.265491901 Reorder the terms: 31 + x = 30.265491901 Solving 31 + x = 30.265491901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = 30.265491901 + -31 Combine like terms: 31 + -31 = 0 0 + x = 30.265491901 + -31 x = 30.265491901 + -31 Combine like terms: 30.265491901 + -31 = -0.734508099 x = -0.734508099 Simplifying x = -0.734508099Subproblem 2
x + 31 = -30.265491901 Simplifying x + 31 = -30.265491901 Reorder the terms: 31 + x = -30.265491901 Solving 31 + x = -30.265491901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = -30.265491901 + -31 Combine like terms: 31 + -31 = 0 0 + x = -30.265491901 + -31 x = -30.265491901 + -31 Combine like terms: -30.265491901 + -31 = -61.265491901 x = -61.265491901 Simplifying x = -61.265491901Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.734508099, -61.265491901}
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