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Simplifying x2 + -567x + 460 = 0 Reorder the terms: 460 + -567x + x2 = 0 Solving 460 + -567x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-460' to each side of the equation. 460 + -567x + -460 + x2 = 0 + -460 Reorder the terms: 460 + -460 + -567x + x2 = 0 + -460 Combine like terms: 460 + -460 = 0 0 + -567x + x2 = 0 + -460 -567x + x2 = 0 + -460 Combine like terms: 0 + -460 = -460 -567x + x2 = -460 The x term is -567x. Take half its coefficient (-283.5). Square it (80372.25) and add it to both sides. Add '80372.25' to each side of the equation. -567x + 80372.25 + x2 = -460 + 80372.25 Reorder the terms: 80372.25 + -567x + x2 = -460 + 80372.25 Combine like terms: -460 + 80372.25 = 79912.25 80372.25 + -567x + x2 = 79912.25 Factor a perfect square on the left side: (x + -283.5)(x + -283.5) = 79912.25 Calculate the square root of the right side: 282.687548364 Break this problem into two subproblems by setting (x + -283.5) equal to 282.687548364 and -282.687548364.Subproblem 1
x + -283.5 = 282.687548364 Simplifying x + -283.5 = 282.687548364 Reorder the terms: -283.5 + x = 282.687548364 Solving -283.5 + x = 282.687548364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '283.5' to each side of the equation. -283.5 + 283.5 + x = 282.687548364 + 283.5 Combine like terms: -283.5 + 283.5 = 0.0 0.0 + x = 282.687548364 + 283.5 x = 282.687548364 + 283.5 Combine like terms: 282.687548364 + 283.5 = 566.187548364 x = 566.187548364 Simplifying x = 566.187548364Subproblem 2
x + -283.5 = -282.687548364 Simplifying x + -283.5 = -282.687548364 Reorder the terms: -283.5 + x = -282.687548364 Solving -283.5 + x = -282.687548364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '283.5' to each side of the equation. -283.5 + 283.5 + x = -282.687548364 + 283.5 Combine like terms: -283.5 + 283.5 = 0.0 0.0 + x = -282.687548364 + 283.5 x = -282.687548364 + 283.5 Combine like terms: -282.687548364 + 283.5 = 0.812451636 x = 0.812451636 Simplifying x = 0.812451636Solution
The solution to the problem is based on the solutions from the subproblems. x = {566.187548364, 0.812451636}
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