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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 = -11.83772234 x = -11.83772234 Simplifying x = -11.83772234Subproblem 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 = -18.16227766 x = -18.16227766 Simplifying x = -18.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-11.83772234, -18.16227766}
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