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Simplifying x2 + -30x + 120 = 0 Reorder the terms: 120 + -30x + x2 = 0 Solving 120 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + -30x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + -30x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -30x + x2 = 0 + -120 -30x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 -30x + x2 = -120 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -120 + 225 Reorder the terms: 225 + -30x + x2 = -120 + 225 Combine like terms: -120 + 225 = 105 225 + -30x + x2 = 105 Factor a perfect square on the left side: (x + -15)(x + -15) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + -15) equal to 10.246950766 and -10.246950766.Subproblem 1
x + -15 = 10.246950766 Simplifying x + -15 = 10.246950766 Reorder the terms: -15 + x = 10.246950766 Solving -15 + x = 10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 10.246950766 + 15 Combine like terms: -15 + 15 = 0 0 + x = 10.246950766 + 15 x = 10.246950766 + 15 Combine like terms: 10.246950766 + 15 = 25.246950766 x = 25.246950766 Simplifying x = 25.246950766Subproblem 2
x + -15 = -10.246950766 Simplifying x + -15 = -10.246950766 Reorder the terms: -15 + x = -10.246950766 Solving -15 + x = -10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -10.246950766 + 15 Combine like terms: -15 + 15 = 0 0 + x = -10.246950766 + 15 x = -10.246950766 + 15 Combine like terms: -10.246950766 + 15 = 4.753049234 x = 4.753049234 Simplifying x = 4.753049234Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.246950766, 4.753049234}
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