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Simplifying 218.25 + 69x + x2 = 0 Solving 218.25 + 69x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-218.25' to each side of the equation. 218.25 + 69x + -218.25 + x2 = 0 + -218.25 Reorder the terms: 218.25 + -218.25 + 69x + x2 = 0 + -218.25 Combine like terms: 218.25 + -218.25 = 0.00 0.00 + 69x + x2 = 0 + -218.25 69x + x2 = 0 + -218.25 Combine like terms: 0 + -218.25 = -218.25 69x + x2 = -218.25 The x term is 69x. Take half its coefficient (34.5). Square it (1190.25) and add it to both sides. Add '1190.25' to each side of the equation. 69x + 1190.25 + x2 = -218.25 + 1190.25 Reorder the terms: 1190.25 + 69x + x2 = -218.25 + 1190.25 Combine like terms: -218.25 + 1190.25 = 972 1190.25 + 69x + x2 = 972 Factor a perfect square on the left side: (x + 34.5)(x + 34.5) = 972 Calculate the square root of the right side: 31.176914536 Break this problem into two subproblems by setting (x + 34.5) equal to 31.176914536 and -31.176914536.Subproblem 1
x + 34.5 = 31.176914536 Simplifying x + 34.5 = 31.176914536 Reorder the terms: 34.5 + x = 31.176914536 Solving 34.5 + x = 31.176914536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.5' to each side of the equation. 34.5 + -34.5 + x = 31.176914536 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + x = 31.176914536 + -34.5 x = 31.176914536 + -34.5 Combine like terms: 31.176914536 + -34.5 = -3.323085464 x = -3.323085464 Simplifying x = -3.323085464Subproblem 2
x + 34.5 = -31.176914536 Simplifying x + 34.5 = -31.176914536 Reorder the terms: 34.5 + x = -31.176914536 Solving 34.5 + x = -31.176914536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.5' to each side of the equation. 34.5 + -34.5 + x = -31.176914536 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + x = -31.176914536 + -34.5 x = -31.176914536 + -34.5 Combine like terms: -31.176914536 + -34.5 = -65.676914536 x = -65.676914536 Simplifying x = -65.676914536Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.323085464, -65.676914536}
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