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Simplifying x2 + -30x = -25 Reorder the terms: -30x + x2 = -25 Solving -30x + x2 = -25 Solving for variable 'x'. Reorder the terms: 25 + -30x + x2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -30x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -30x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -30x + x2 = 0 + -25 -30x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -30x + x2 = -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 = -25 + 225 Reorder the terms: 225 + -30x + x2 = -25 + 225 Combine like terms: -25 + 225 = 200 225 + -30x + x2 = 200 Factor a perfect square on the left side: (x + -15)(x + -15) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + -15) equal to 14.142135624 and -14.142135624.Subproblem 1
x + -15 = 14.142135624 Simplifying x + -15 = 14.142135624 Reorder the terms: -15 + x = 14.142135624 Solving -15 + x = 14.142135624 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 = 14.142135624 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.142135624 + 15 x = 14.142135624 + 15 Combine like terms: 14.142135624 + 15 = 29.142135624 x = 29.142135624 Simplifying x = 29.142135624Subproblem 2
x + -15 = -14.142135624 Simplifying x + -15 = -14.142135624 Reorder the terms: -15 + x = -14.142135624 Solving -15 + x = -14.142135624 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 = -14.142135624 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.142135624 + 15 x = -14.142135624 + 15 Combine like terms: -14.142135624 + 15 = 0.857864376 x = 0.857864376 Simplifying x = 0.857864376Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.142135624, 0.857864376}
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