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Simplifying x2 + -30x + 215 = 0 Reorder the terms: 215 + -30x + x2 = 0 Solving 215 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-215' to each side of the equation. 215 + -30x + -215 + x2 = 0 + -215 Reorder the terms: 215 + -215 + -30x + x2 = 0 + -215 Combine like terms: 215 + -215 = 0 0 + -30x + x2 = 0 + -215 -30x + x2 = 0 + -215 Combine like terms: 0 + -215 = -215 -30x + x2 = -215 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 = -215 + 225 Reorder the terms: 225 + -30x + x2 = -215 + 225 Combine like terms: -215 + 225 = 10 225 + -30x + x2 = 10 Factor a perfect square on the left side: (x + -15)(x + -15) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -15) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -15 = 3.16227766 Simplifying x + -15 = 3.16227766 Reorder the terms: -15 + x = 3.16227766 Solving -15 + x = 3.16227766 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 = 3.16227766 + 15 Combine like terms: -15 + 15 = 0 0 + x = 3.16227766 + 15 x = 3.16227766 + 15 Combine like terms: 3.16227766 + 15 = 18.16227766 x = 18.16227766 Simplifying x = 18.16227766Subproblem 2
x + -15 = -3.16227766 Simplifying x + -15 = -3.16227766 Reorder the terms: -15 + x = -3.16227766 Solving -15 + x = -3.16227766 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 = -3.16227766 + 15 Combine like terms: -15 + 15 = 0 0 + x = -3.16227766 + 15 x = -3.16227766 + 15 Combine like terms: -3.16227766 + 15 = 11.83772234 x = 11.83772234 Simplifying x = 11.83772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.16227766, 11.83772234}
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