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Simplifying x2 + -30x + -29 = 0 Reorder the terms: -29 + -30x + x2 = 0 Solving -29 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -30x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -30x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -30x + x2 = 0 + 29 -30x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -30x + x2 = 29 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 = 29 + 225 Reorder the terms: 225 + -30x + x2 = 29 + 225 Combine like terms: 29 + 225 = 254 225 + -30x + x2 = 254 Factor a perfect square on the left side: (x + -15)(x + -15) = 254 Calculate the square root of the right side: 15.937377451 Break this problem into two subproblems by setting (x + -15) equal to 15.937377451 and -15.937377451.Subproblem 1
x + -15 = 15.937377451 Simplifying x + -15 = 15.937377451 Reorder the terms: -15 + x = 15.937377451 Solving -15 + x = 15.937377451 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 = 15.937377451 + 15 Combine like terms: -15 + 15 = 0 0 + x = 15.937377451 + 15 x = 15.937377451 + 15 Combine like terms: 15.937377451 + 15 = 30.937377451 x = 30.937377451 Simplifying x = 30.937377451Subproblem 2
x + -15 = -15.937377451 Simplifying x + -15 = -15.937377451 Reorder the terms: -15 + x = -15.937377451 Solving -15 + x = -15.937377451 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 = -15.937377451 + 15 Combine like terms: -15 + 15 = 0 0 + x = -15.937377451 + 15 x = -15.937377451 + 15 Combine like terms: -15.937377451 + 15 = -0.937377451 x = -0.937377451 Simplifying x = -0.937377451Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.937377451, -0.937377451}
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