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Simplifying x2 + -30x = 125 Reorder the terms: -30x + x2 = 125 Solving -30x + x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + -30x + x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + -30x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -30x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -30x + x2 = 0 + 125 -30x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -30x + x2 = 125 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 = 125 + 225 Reorder the terms: 225 + -30x + x2 = 125 + 225 Combine like terms: 125 + 225 = 350 225 + -30x + x2 = 350 Factor a perfect square on the left side: (x + -15)(x + -15) = 350 Calculate the square root of the right side: 18.708286934 Break this problem into two subproblems by setting (x + -15) equal to 18.708286934 and -18.708286934.Subproblem 1
x + -15 = 18.708286934 Simplifying x + -15 = 18.708286934 Reorder the terms: -15 + x = 18.708286934 Solving -15 + x = 18.708286934 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 = 18.708286934 + 15 Combine like terms: -15 + 15 = 0 0 + x = 18.708286934 + 15 x = 18.708286934 + 15 Combine like terms: 18.708286934 + 15 = 33.708286934 x = 33.708286934 Simplifying x = 33.708286934Subproblem 2
x + -15 = -18.708286934 Simplifying x + -15 = -18.708286934 Reorder the terms: -15 + x = -18.708286934 Solving -15 + x = -18.708286934 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 = -18.708286934 + 15 Combine like terms: -15 + 15 = 0 0 + x = -18.708286934 + 15 x = -18.708286934 + 15 Combine like terms: -18.708286934 + 15 = -3.708286934 x = -3.708286934 Simplifying x = -3.708286934Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.708286934, -3.708286934}
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