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Simplifying x(x + 30) = 150 Reorder the terms: x(30 + x) = 150 (30 * x + x * x) = 150 (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 = 375 225 + 30x + x2 = 375 Factor a perfect square on the left side: (x + 15)(x + 15) = 375 Calculate the square root of the right side: 19.364916731 Break this problem into two subproblems by setting (x + 15) equal to 19.364916731 and -19.364916731.Subproblem 1
x + 15 = 19.364916731 Simplifying x + 15 = 19.364916731 Reorder the terms: 15 + x = 19.364916731 Solving 15 + x = 19.364916731 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 = 19.364916731 + -15 Combine like terms: 15 + -15 = 0 0 + x = 19.364916731 + -15 x = 19.364916731 + -15 Combine like terms: 19.364916731 + -15 = 4.364916731 x = 4.364916731 Simplifying x = 4.364916731Subproblem 2
x + 15 = -19.364916731 Simplifying x + 15 = -19.364916731 Reorder the terms: 15 + x = -19.364916731 Solving 15 + x = -19.364916731 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 = -19.364916731 + -15 Combine like terms: 15 + -15 = 0 0 + x = -19.364916731 + -15 x = -19.364916731 + -15 Combine like terms: -19.364916731 + -15 = -34.364916731 x = -34.364916731 Simplifying x = -34.364916731Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.364916731, -34.364916731}
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