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Simplifying 8.156x2 + -5.7092x + 0.97872 = 0 Reorder the terms: 0.97872 + -5.7092x + 8.156x2 = 0 Solving 0.97872 + -5.7092x + 8.156x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8.156 the coefficient of the squared term: Divide each side by '8.156'. 0.12 + -0.7x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.7x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.7x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.7x + x2 = 0 + -0.12 -0.7x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.7x + x2 = -0.12 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = -0.12 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = -0.12 + 0.1225 Combine like terms: -0.12 + 0.1225 = 0.0025 0.1225 + -0.7x + x2 = 0.0025 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 0.0025 Calculate the square root of the right side: 0.05 Break this problem into two subproblems by setting (x + -0.35) equal to 0.05 and -0.05.Subproblem 1
x + -0.35 = 0.05 Simplifying x + -0.35 = 0.05 Reorder the terms: -0.35 + x = 0.05 Solving -0.35 + x = 0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 0.05 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.05 + 0.35 x = 0.05 + 0.35 Combine like terms: 0.05 + 0.35 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + -0.35 = -0.05 Simplifying x + -0.35 = -0.05 Reorder the terms: -0.35 + x = -0.05 Solving -0.35 + x = -0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -0.05 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -0.05 + 0.35 x = -0.05 + 0.35 Combine like terms: -0.05 + 0.35 = 0.3 x = 0.3 Simplifying x = 0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, 0.3}
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