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Simplifying -0.05x2 + 0.86x + 1.2 = 0 Reorder the terms: 1.2 + 0.86x + -0.05x2 = 0 Solving 1.2 + 0.86x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -24 + -17.2x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -17.2x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -17.2x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -17.2x + x2 = 0 + 24 -17.2x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -17.2x + x2 = 24 The x term is -17.2x. Take half its coefficient (-8.6). Square it (73.96) and add it to both sides. Add '73.96' to each side of the equation. -17.2x + 73.96 + x2 = 24 + 73.96 Reorder the terms: 73.96 + -17.2x + x2 = 24 + 73.96 Combine like terms: 24 + 73.96 = 97.96 73.96 + -17.2x + x2 = 97.96 Factor a perfect square on the left side: (x + -8.6)(x + -8.6) = 97.96 Calculate the square root of the right side: 9.897474425 Break this problem into two subproblems by setting (x + -8.6) equal to 9.897474425 and -9.897474425.Subproblem 1
x + -8.6 = 9.897474425 Simplifying x + -8.6 = 9.897474425 Reorder the terms: -8.6 + x = 9.897474425 Solving -8.6 + x = 9.897474425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.6' to each side of the equation. -8.6 + 8.6 + x = 9.897474425 + 8.6 Combine like terms: -8.6 + 8.6 = 0.0 0.0 + x = 9.897474425 + 8.6 x = 9.897474425 + 8.6 Combine like terms: 9.897474425 + 8.6 = 18.497474425 x = 18.497474425 Simplifying x = 18.497474425Subproblem 2
x + -8.6 = -9.897474425 Simplifying x + -8.6 = -9.897474425 Reorder the terms: -8.6 + x = -9.897474425 Solving -8.6 + x = -9.897474425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.6' to each side of the equation. -8.6 + 8.6 + x = -9.897474425 + 8.6 Combine like terms: -8.6 + 8.6 = 0.0 0.0 + x = -9.897474425 + 8.6 x = -9.897474425 + 8.6 Combine like terms: -9.897474425 + 8.6 = -1.297474425 x = -1.297474425 Simplifying x = -1.297474425Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.497474425, -1.297474425}
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