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Simplifying 0 = -1x2 + 30x + -150 Reorder the terms: 0 = -150 + 30x + -1x2 Solving 0 = -150 + 30x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 150 = 150 150 + -30x + x2 = -150 + 30x + -1x2 + 150 + -30x + x2 Reorder the terms: 150 + -30x + x2 = -150 + 150 + 30x + -30x + -1x2 + x2 Combine like terms: -150 + 150 = 0 150 + -30x + x2 = 0 + 30x + -30x + -1x2 + x2 150 + -30x + x2 = 30x + -30x + -1x2 + x2 Combine like terms: 30x + -30x = 0 150 + -30x + x2 = 0 + -1x2 + x2 150 + -30x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 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 = 23.660254038 x = 23.660254038 Simplifying x = 23.660254038Subproblem 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 = 6.339745962 x = 6.339745962 Simplifying x = 6.339745962Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.660254038, 6.339745962}
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