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Simplifying 4x2 + -32x + 256 = 15 + 256 Reorder the terms: 256 + -32x + 4x2 = 15 + 256 Combine like terms: 15 + 256 = 271 256 + -32x + 4x2 = 271 Solving 256 + -32x + 4x2 = 271 Solving for variable 'x'. Reorder the terms: 256 + -271 + -32x + 4x2 = 271 + -271 Combine like terms: 256 + -271 = -15 -15 + -32x + 4x2 = 271 + -271 Combine like terms: 271 + -271 = 0 -15 + -32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -8x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -8x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -8x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -8x + x2 = 0 + 3.75 -8x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -8x + x2 = 3.75 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 3.75 + 16 Reorder the terms: 16 + -8x + x2 = 3.75 + 16 Combine like terms: 3.75 + 16 = 19.75 16 + -8x + x2 = 19.75 Factor a perfect square on the left side: (x + -4)(x + -4) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + -4) equal to 4.444097209 and -4.444097209.Subproblem 1
x + -4 = 4.444097209 Simplifying x + -4 = 4.444097209 Reorder the terms: -4 + x = 4.444097209 Solving -4 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.444097209 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.444097209 + 4 x = 4.444097209 + 4 Combine like terms: 4.444097209 + 4 = 8.444097209 x = 8.444097209 Simplifying x = 8.444097209Subproblem 2
x + -4 = -4.444097209 Simplifying x + -4 = -4.444097209 Reorder the terms: -4 + x = -4.444097209 Solving -4 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.444097209 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.444097209 + 4 x = -4.444097209 + 4 Combine like terms: -4.444097209 + 4 = -0.444097209 x = -0.444097209 Simplifying x = -0.444097209Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.444097209, -0.444097209}
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