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Simplifying x2 + -8x + 16 = 15.625 Reorder the terms: 16 + -8x + x2 = 15.625 Solving 16 + -8x + x2 = 15.625 Solving for variable 'x'. Reorder the terms: 16 + -15.625 + -8x + x2 = 15.625 + -15.625 Combine like terms: 16 + -15.625 = 0.375 0.375 + -8x + x2 = 15.625 + -15.625 Combine like terms: 15.625 + -15.625 = 0.000 0.375 + -8x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -8x + -0.375 + x2 = 0.000 + -0.375 Reorder the terms: 0.375 + -0.375 + -8x + x2 = 0.000 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -8x + x2 = 0.000 + -0.375 -8x + x2 = 0.000 + -0.375 Combine like terms: 0.000 + -0.375 = -0.375 -8x + x2 = -0.375 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 = -0.375 + 16 Reorder the terms: 16 + -8x + x2 = -0.375 + 16 Combine like terms: -0.375 + 16 = 15.625 16 + -8x + x2 = 15.625 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.625 Calculate the square root of the right side: 3.952847075 Break this problem into two subproblems by setting (x + -4) equal to 3.952847075 and -3.952847075.Subproblem 1
x + -4 = 3.952847075 Simplifying x + -4 = 3.952847075 Reorder the terms: -4 + x = 3.952847075 Solving -4 + x = 3.952847075 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 = 3.952847075 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.952847075 + 4 x = 3.952847075 + 4 Combine like terms: 3.952847075 + 4 = 7.952847075 x = 7.952847075 Simplifying x = 7.952847075Subproblem 2
x + -4 = -3.952847075 Simplifying x + -4 = -3.952847075 Reorder the terms: -4 + x = -3.952847075 Solving -4 + x = -3.952847075 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 = -3.952847075 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.952847075 + 4 x = -3.952847075 + 4 Combine like terms: -3.952847075 + 4 = 0.047152925 x = 0.047152925 Simplifying x = 0.047152925Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.952847075, 0.047152925}
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