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Simplifying x2 + -8x + 3.2 = 0.8 Reorder the terms: 3.2 + -8x + x2 = 0.8 Solving 3.2 + -8x + x2 = 0.8 Solving for variable 'x'. Reorder the terms: 3.2 + -0.8 + -8x + x2 = 0.8 + -0.8 Combine like terms: 3.2 + -0.8 = 2.4 2.4 + -8x + x2 = 0.8 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 2.4 + -8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -8x + -2.4 + x2 = 0.0 + -2.4 Reorder the terms: 2.4 + -2.4 + -8x + x2 = 0.0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -8x + x2 = 0.0 + -2.4 -8x + x2 = 0.0 + -2.4 Combine like terms: 0.0 + -2.4 = -2.4 -8x + x2 = -2.4 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 = -2.4 + 16 Reorder the terms: 16 + -8x + x2 = -2.4 + 16 Combine like terms: -2.4 + 16 = 13.6 16 + -8x + x2 = 13.6 Factor a perfect square on the left side: (x + -4)(x + -4) = 13.6 Calculate the square root of the right side: 3.687817783 Break this problem into two subproblems by setting (x + -4) equal to 3.687817783 and -3.687817783.Subproblem 1
x + -4 = 3.687817783 Simplifying x + -4 = 3.687817783 Reorder the terms: -4 + x = 3.687817783 Solving -4 + x = 3.687817783 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 = 3.687817783 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.687817783 + 4 x = 3.687817783 + 4 Combine like terms: 3.687817783 + 4 = 7.687817783 x = 7.687817783 Simplifying x = 7.687817783Subproblem 2
x + -4 = -3.687817783 Simplifying x + -4 = -3.687817783 Reorder the terms: -4 + x = -3.687817783 Solving -4 + x = -3.687817783 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 = -3.687817783 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.687817783 + 4 x = -3.687817783 + 4 Combine like terms: -3.687817783 + 4 = 0.312182217 x = 0.312182217 Simplifying x = 0.312182217Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.687817783, 0.312182217}
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