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Simplifying x2 + -30x + -63 = 0 Reorder the terms: -63 + -30x + x2 = 0 Solving -63 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -30x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + -30x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -30x + x2 = 0 + 63 -30x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 -30x + x2 = 63 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 = 63 + 225 Reorder the terms: 225 + -30x + x2 = 63 + 225 Combine like terms: 63 + 225 = 288 225 + -30x + x2 = 288 Factor a perfect square on the left side: (x + -15)(x + -15) = 288 Calculate the square root of the right side: 16.970562748 Break this problem into two subproblems by setting (x + -15) equal to 16.970562748 and -16.970562748.Subproblem 1
x + -15 = 16.970562748 Simplifying x + -15 = 16.970562748 Reorder the terms: -15 + x = 16.970562748 Solving -15 + x = 16.970562748 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 = 16.970562748 + 15 Combine like terms: -15 + 15 = 0 0 + x = 16.970562748 + 15 x = 16.970562748 + 15 Combine like terms: 16.970562748 + 15 = 31.970562748 x = 31.970562748 Simplifying x = 31.970562748Subproblem 2
x + -15 = -16.970562748 Simplifying x + -15 = -16.970562748 Reorder the terms: -15 + x = -16.970562748 Solving -15 + x = -16.970562748 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 = -16.970562748 + 15 Combine like terms: -15 + 15 = 0 0 + x = -16.970562748 + 15 x = -16.970562748 + 15 Combine like terms: -16.970562748 + 15 = -1.970562748 x = -1.970562748 Simplifying x = -1.970562748Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.970562748, -1.970562748}
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