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Simplifying x2 + -30x + 90 = 0 Reorder the terms: 90 + -30x + x2 = 0 Solving 90 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + -30x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -30x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -30x + x2 = 0 + -90 -30x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -30x + x2 = -90 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 = -90 + 225 Reorder the terms: 225 + -30x + x2 = -90 + 225 Combine like terms: -90 + 225 = 135 225 + -30x + x2 = 135 Factor a perfect square on the left side: (x + -15)(x + -15) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (x + -15) equal to 11.618950039 and -11.618950039.Subproblem 1
x + -15 = 11.618950039 Simplifying x + -15 = 11.618950039 Reorder the terms: -15 + x = 11.618950039 Solving -15 + x = 11.618950039 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 = 11.618950039 + 15 Combine like terms: -15 + 15 = 0 0 + x = 11.618950039 + 15 x = 11.618950039 + 15 Combine like terms: 11.618950039 + 15 = 26.618950039 x = 26.618950039 Simplifying x = 26.618950039Subproblem 2
x + -15 = -11.618950039 Simplifying x + -15 = -11.618950039 Reorder the terms: -15 + x = -11.618950039 Solving -15 + x = -11.618950039 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 = -11.618950039 + 15 Combine like terms: -15 + 15 = 0 0 + x = -11.618950039 + 15 x = -11.618950039 + 15 Combine like terms: -11.618950039 + 15 = 3.381049961 x = 3.381049961 Simplifying x = 3.381049961Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.618950039, 3.381049961}
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