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Simplifying 0.25x2 + -8x + -45 = 0 Reorder the terms: -45 + -8x + 0.25x2 = 0 Solving -45 + -8x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -180 + -32x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + -32x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -32x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -32x + x2 = 0 + 180 -32x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -32x + x2 = 180 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 180 + 256 Reorder the terms: 256 + -32x + x2 = 180 + 256 Combine like terms: 180 + 256 = 436 256 + -32x + x2 = 436 Factor a perfect square on the left side: (x + -16)(x + -16) = 436 Calculate the square root of the right side: 20.880613018 Break this problem into two subproblems by setting (x + -16) equal to 20.880613018 and -20.880613018.Subproblem 1
x + -16 = 20.880613018 Simplifying x + -16 = 20.880613018 Reorder the terms: -16 + x = 20.880613018 Solving -16 + x = 20.880613018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 20.880613018 + 16 Combine like terms: -16 + 16 = 0 0 + x = 20.880613018 + 16 x = 20.880613018 + 16 Combine like terms: 20.880613018 + 16 = 36.880613018 x = 36.880613018 Simplifying x = 36.880613018Subproblem 2
x + -16 = -20.880613018 Simplifying x + -16 = -20.880613018 Reorder the terms: -16 + x = -20.880613018 Solving -16 + x = -20.880613018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -20.880613018 + 16 Combine like terms: -16 + 16 = 0 0 + x = -20.880613018 + 16 x = -20.880613018 + 16 Combine like terms: -20.880613018 + 16 = -4.880613018 x = -4.880613018 Simplifying x = -4.880613018Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.880613018, -4.880613018}
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