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Simplifying 10x2 + -8x + 0.8 = 0 Reorder the terms: 0.8 + -8x + 10x2 = 0 Solving 0.8 + -8x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.08 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + -0.8x + -0.08 + x2 = 0 + -0.08 Reorder the terms: 0.08 + -0.08 + -0.8x + x2 = 0 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + -0.8x + x2 = 0 + -0.08 -0.8x + x2 = 0 + -0.08 Combine like terms: 0 + -0.08 = -0.08 -0.8x + x2 = -0.08 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.08 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.08 + 0.16 Combine like terms: -0.08 + 0.16 = 0.08 0.16 + -0.8x + x2 = 0.08 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.08 Calculate the square root of the right side: 0.282842712 Break this problem into two subproblems by setting (x + -0.4) equal to 0.282842712 and -0.282842712.Subproblem 1
x + -0.4 = 0.282842712 Simplifying x + -0.4 = 0.282842712 Reorder the terms: -0.4 + x = 0.282842712 Solving -0.4 + x = 0.282842712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.282842712 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.282842712 + 0.4 x = 0.282842712 + 0.4 Combine like terms: 0.282842712 + 0.4 = 0.682842712 x = 0.682842712 Simplifying x = 0.682842712Subproblem 2
x + -0.4 = -0.282842712 Simplifying x + -0.4 = -0.282842712 Reorder the terms: -0.4 + x = -0.282842712 Solving -0.4 + x = -0.282842712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.282842712 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.282842712 + 0.4 x = -0.282842712 + 0.4 Combine like terms: -0.282842712 + 0.4 = 0.117157288 x = 0.117157288 Simplifying x = 0.117157288Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.682842712, 0.117157288}
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