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Simplifying x2 + -45x + 150 = 0 Reorder the terms: 150 + -45x + x2 = 0 Solving 150 + -45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-150' to each side of the equation. 150 + -45x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -45x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -45x + x2 = 0 + -150 -45x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -45x + x2 = -150 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = -150 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -150 + 506.25 Combine like terms: -150 + 506.25 = 356.25 506.25 + -45x + x2 = 356.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 356.25 Calculate the square root of the right side: 18.874586088 Break this problem into two subproblems by setting (x + -22.5) equal to 18.874586088 and -18.874586088.Subproblem 1
x + -22.5 = 18.874586088 Simplifying x + -22.5 = 18.874586088 Reorder the terms: -22.5 + x = 18.874586088 Solving -22.5 + x = 18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 18.874586088 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 18.874586088 + 22.5 x = 18.874586088 + 22.5 Combine like terms: 18.874586088 + 22.5 = 41.374586088 x = 41.374586088 Simplifying x = 41.374586088Subproblem 2
x + -22.5 = -18.874586088 Simplifying x + -22.5 = -18.874586088 Reorder the terms: -22.5 + x = -18.874586088 Solving -22.5 + x = -18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -18.874586088 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -18.874586088 + 22.5 x = -18.874586088 + 22.5 Combine like terms: -18.874586088 + 22.5 = 3.625413912 x = 3.625413912 Simplifying x = 3.625413912Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.374586088, 3.625413912}
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