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Simplifying x2 + 30x + 150 = 0.75 Reorder the terms: 150 + 30x + x2 = 0.75 Solving 150 + 30x + x2 = 0.75 Solving for variable 'x'. Reorder the terms: 150 + -0.75 + 30x + x2 = 0.75 + -0.75 Combine like terms: 150 + -0.75 = 149.25 149.25 + 30x + x2 = 0.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 149.25 + 30x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-149.25' to each side of the equation. 149.25 + 30x + -149.25 + x2 = 0.00 + -149.25 Reorder the terms: 149.25 + -149.25 + 30x + x2 = 0.00 + -149.25 Combine like terms: 149.25 + -149.25 = 0.00 0.00 + 30x + x2 = 0.00 + -149.25 30x + x2 = 0.00 + -149.25 Combine like terms: 0.00 + -149.25 = -149.25 30x + x2 = -149.25 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 = -149.25 + 225 Reorder the terms: 225 + 30x + x2 = -149.25 + 225 Combine like terms: -149.25 + 225 = 75.75 225 + 30x + x2 = 75.75 Factor a perfect square on the left side: (x + 15)(x + 15) = 75.75 Calculate the square root of the right side: 8.703447593 Break this problem into two subproblems by setting (x + 15) equal to 8.703447593 and -8.703447593.Subproblem 1
x + 15 = 8.703447593 Simplifying x + 15 = 8.703447593 Reorder the terms: 15 + x = 8.703447593 Solving 15 + x = 8.703447593 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 = 8.703447593 + -15 Combine like terms: 15 + -15 = 0 0 + x = 8.703447593 + -15 x = 8.703447593 + -15 Combine like terms: 8.703447593 + -15 = -6.296552407 x = -6.296552407 Simplifying x = -6.296552407Subproblem 2
x + 15 = -8.703447593 Simplifying x + 15 = -8.703447593 Reorder the terms: 15 + x = -8.703447593 Solving 15 + x = -8.703447593 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 = -8.703447593 + -15 Combine like terms: 15 + -15 = 0 0 + x = -8.703447593 + -15 x = -8.703447593 + -15 Combine like terms: -8.703447593 + -15 = -23.703447593 x = -23.703447593 Simplifying x = -23.703447593Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.296552407, -23.703447593}
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