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Simplifying x2 + -8x + 0.5625 = 0 Reorder the terms: 0.5625 + -8x + x2 = 0 Solving 0.5625 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + -8x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + -8x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + -8x + x2 = 0 + -0.5625 -8x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 -8x + x2 = -0.5625 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 = -0.5625 + 16 Reorder the terms: 16 + -8x + x2 = -0.5625 + 16 Combine like terms: -0.5625 + 16 = 15.4375 16 + -8x + x2 = 15.4375 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.4375 Calculate the square root of the right side: 3.929058411 Break this problem into two subproblems by setting (x + -4) equal to 3.929058411 and -3.929058411.Subproblem 1
x + -4 = 3.929058411 Simplifying x + -4 = 3.929058411 Reorder the terms: -4 + x = 3.929058411 Solving -4 + x = 3.929058411 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 = 3.929058411 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.929058411 + 4 x = 3.929058411 + 4 Combine like terms: 3.929058411 + 4 = 7.929058411 x = 7.929058411 Simplifying x = 7.929058411Subproblem 2
x + -4 = -3.929058411 Simplifying x + -4 = -3.929058411 Reorder the terms: -4 + x = -3.929058411 Solving -4 + x = -3.929058411 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 = -3.929058411 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.929058411 + 4 x = -3.929058411 + 4 Combine like terms: -3.929058411 + 4 = 0.070941589 x = 0.070941589 Simplifying x = 0.070941589Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.929058411, 0.070941589}
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