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Simplifying x2 + -45x + 15 = 0 Reorder the terms: 15 + -45x + x2 = 0 Solving 15 + -45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -45x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -45x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -45x + x2 = 0 + -15 -45x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -45x + x2 = -15 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 = -15 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -15 + 506.25 Combine like terms: -15 + 506.25 = 491.25 506.25 + -45x + x2 = 491.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 491.25 Calculate the square root of the right side: 22.164160259 Break this problem into two subproblems by setting (x + -22.5) equal to 22.164160259 and -22.164160259.Subproblem 1
x + -22.5 = 22.164160259 Simplifying x + -22.5 = 22.164160259 Reorder the terms: -22.5 + x = 22.164160259 Solving -22.5 + x = 22.164160259 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 = 22.164160259 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 22.164160259 + 22.5 x = 22.164160259 + 22.5 Combine like terms: 22.164160259 + 22.5 = 44.664160259 x = 44.664160259 Simplifying x = 44.664160259Subproblem 2
x + -22.5 = -22.164160259 Simplifying x + -22.5 = -22.164160259 Reorder the terms: -22.5 + x = -22.164160259 Solving -22.5 + x = -22.164160259 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 = -22.164160259 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -22.164160259 + 22.5 x = -22.164160259 + 22.5 Combine like terms: -22.164160259 + 22.5 = 0.335839741 x = 0.335839741 Simplifying x = 0.335839741Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.664160259, 0.335839741}
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