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Simplifying x2 + 30x = -150 Reorder the terms: 30x + x2 = -150 Solving 30x + x2 = -150 Solving for variable 'x'. Reorder the terms: 150 + 30x + x2 = -150 + 150 Combine like terms: -150 + 150 = 0 150 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-150' to each side of the equation. 150 + 30x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + 30x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + 30x + x2 = 0 + -150 30x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 30x + x2 = -150 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 = -150 + 225 Reorder the terms: 225 + 30x + x2 = -150 + 225 Combine like terms: -150 + 225 = 75 225 + 30x + x2 = 75 Factor a perfect square on the left side: (x + 15)(x + 15) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + 15) equal to 8.660254038 and -8.660254038.Subproblem 1
x + 15 = 8.660254038 Simplifying x + 15 = 8.660254038 Reorder the terms: 15 + x = 8.660254038 Solving 15 + x = 8.660254038 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 = 8.660254038 + -15 Combine like terms: 15 + -15 = 0 0 + x = 8.660254038 + -15 x = 8.660254038 + -15 Combine like terms: 8.660254038 + -15 = -6.339745962 x = -6.339745962 Simplifying x = -6.339745962Subproblem 2
x + 15 = -8.660254038 Simplifying x + 15 = -8.660254038 Reorder the terms: 15 + x = -8.660254038 Solving 15 + x = -8.660254038 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 = -8.660254038 + -15 Combine like terms: 15 + -15 = 0 0 + x = -8.660254038 + -15 x = -8.660254038 + -15 Combine like terms: -8.660254038 + -15 = -23.660254038 x = -23.660254038 Simplifying x = -23.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.339745962, -23.660254038}
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