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Simplifying -150 = 45x + -1x2 Solving -150 = 45x + -1x2 Solving for variable 'x'. Reorder the terms: -150 + -45x + x2 = 45x + -45x + -1x2 + x2 Combine like terms: 45x + -45x = 0 -150 + -45x + x2 = 0 + -1x2 + x2 -150 + -45x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -150 + -45x + x2 = 0 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 = 656.25 506.25 + -45x + x2 = 656.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 656.25 Calculate the square root of the right side: 25.617376915 Break this problem into two subproblems by setting (x + -22.5) equal to 25.617376915 and -25.617376915.Subproblem 1
x + -22.5 = 25.617376915 Simplifying x + -22.5 = 25.617376915 Reorder the terms: -22.5 + x = 25.617376915 Solving -22.5 + x = 25.617376915 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 = 25.617376915 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 25.617376915 + 22.5 x = 25.617376915 + 22.5 Combine like terms: 25.617376915 + 22.5 = 48.117376915 x = 48.117376915 Simplifying x = 48.117376915Subproblem 2
x + -22.5 = -25.617376915 Simplifying x + -22.5 = -25.617376915 Reorder the terms: -22.5 + x = -25.617376915 Solving -22.5 + x = -25.617376915 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 = -25.617376915 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -25.617376915 + 22.5 x = -25.617376915 + 22.5 Combine like terms: -25.617376915 + 22.5 = -3.117376915 x = -3.117376915 Simplifying x = -3.117376915Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.117376915, -3.117376915}
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