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Simplifying x2 + -30x + 218.75 = 0 Reorder the terms: 218.75 + -30x + x2 = 0 Solving 218.75 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-218.75' to each side of the equation. 218.75 + -30x + -218.75 + x2 = 0 + -218.75 Reorder the terms: 218.75 + -218.75 + -30x + x2 = 0 + -218.75 Combine like terms: 218.75 + -218.75 = 0.00 0.00 + -30x + x2 = 0 + -218.75 -30x + x2 = 0 + -218.75 Combine like terms: 0 + -218.75 = -218.75 -30x + x2 = -218.75 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 = -218.75 + 225 Reorder the terms: 225 + -30x + x2 = -218.75 + 225 Combine like terms: -218.75 + 225 = 6.25 225 + -30x + x2 = 6.25 Factor a perfect square on the left side: (x + -15)(x + -15) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -15) equal to 2.5 and -2.5.Subproblem 1
x + -15 = 2.5 Simplifying x + -15 = 2.5 Reorder the terms: -15 + x = 2.5 Solving -15 + x = 2.5 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 = 2.5 + 15 Combine like terms: -15 + 15 = 0 0 + x = 2.5 + 15 x = 2.5 + 15 Combine like terms: 2.5 + 15 = 17.5 x = 17.5 Simplifying x = 17.5Subproblem 2
x + -15 = -2.5 Simplifying x + -15 = -2.5 Reorder the terms: -15 + x = -2.5 Solving -15 + x = -2.5 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 = -2.5 + 15 Combine like terms: -15 + 15 = 0 0 + x = -2.5 + 15 x = -2.5 + 15 Combine like terms: -2.5 + 15 = 12.5 x = 12.5 Simplifying x = 12.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.5, 12.5}
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