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Simplifying x2 + -30x + 255 = 400 Reorder the terms: 255 + -30x + x2 = 400 Solving 255 + -30x + x2 = 400 Solving for variable 'x'. Reorder the terms: 255 + -400 + -30x + x2 = 400 + -400 Combine like terms: 255 + -400 = -145 -145 + -30x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -145 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '145' to each side of the equation. -145 + -30x + 145 + x2 = 0 + 145 Reorder the terms: -145 + 145 + -30x + x2 = 0 + 145 Combine like terms: -145 + 145 = 0 0 + -30x + x2 = 0 + 145 -30x + x2 = 0 + 145 Combine like terms: 0 + 145 = 145 -30x + x2 = 145 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 = 145 + 225 Reorder the terms: 225 + -30x + x2 = 145 + 225 Combine like terms: 145 + 225 = 370 225 + -30x + x2 = 370 Factor a perfect square on the left side: (x + -15)(x + -15) = 370 Calculate the square root of the right side: 19.235384062 Break this problem into two subproblems by setting (x + -15) equal to 19.235384062 and -19.235384062.Subproblem 1
x + -15 = 19.235384062 Simplifying x + -15 = 19.235384062 Reorder the terms: -15 + x = 19.235384062 Solving -15 + x = 19.235384062 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 = 19.235384062 + 15 Combine like terms: -15 + 15 = 0 0 + x = 19.235384062 + 15 x = 19.235384062 + 15 Combine like terms: 19.235384062 + 15 = 34.235384062 x = 34.235384062 Simplifying x = 34.235384062Subproblem 2
x + -15 = -19.235384062 Simplifying x + -15 = -19.235384062 Reorder the terms: -15 + x = -19.235384062 Solving -15 + x = -19.235384062 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 = -19.235384062 + 15 Combine like terms: -15 + 15 = 0 0 + x = -19.235384062 + 15 x = -19.235384062 + 15 Combine like terms: -19.235384062 + 15 = -4.235384062 x = -4.235384062 Simplifying x = -4.235384062Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.235384062, -4.235384062}
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