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Simplifying x2 + -30x + -112.5 = 0 Reorder the terms: -112.5 + -30x + x2 = 0 Solving -112.5 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + -30x + 112.5 + x2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + -30x + x2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + -30x + x2 = 0 + 112.5 -30x + x2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 -30x + x2 = 112.5 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 = 112.5 + 225 Reorder the terms: 225 + -30x + x2 = 112.5 + 225 Combine like terms: 112.5 + 225 = 337.5 225 + -30x + x2 = 337.5 Factor a perfect square on the left side: (x + -15)(x + -15) = 337.5 Calculate the square root of the right side: 18.371173071 Break this problem into two subproblems by setting (x + -15) equal to 18.371173071 and -18.371173071.Subproblem 1
x + -15 = 18.371173071 Simplifying x + -15 = 18.371173071 Reorder the terms: -15 + x = 18.371173071 Solving -15 + x = 18.371173071 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 = 18.371173071 + 15 Combine like terms: -15 + 15 = 0 0 + x = 18.371173071 + 15 x = 18.371173071 + 15 Combine like terms: 18.371173071 + 15 = 33.371173071 x = 33.371173071 Simplifying x = 33.371173071Subproblem 2
x + -15 = -18.371173071 Simplifying x + -15 = -18.371173071 Reorder the terms: -15 + x = -18.371173071 Solving -15 + x = -18.371173071 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 = -18.371173071 + 15 Combine like terms: -15 + 15 = 0 0 + x = -18.371173071 + 15 x = -18.371173071 + 15 Combine like terms: -18.371173071 + 15 = -3.371173071 x = -3.371173071 Simplifying x = -3.371173071Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.371173071, -3.371173071}
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