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Simplifying -16.1x2 + 4x + 32.6 = 0 Reorder the terms: 32.6 + 4x + -16.1x2 = 0 Solving 32.6 + 4x + -16.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16.1 the coefficient of the squared term: Divide each side by '-16.1'. -2.02484472 + -0.248447205x + x2 = 0 Move the constant term to the right: Add '2.02484472' to each side of the equation. -2.02484472 + -0.248447205x + 2.02484472 + x2 = 0 + 2.02484472 Reorder the terms: -2.02484472 + 2.02484472 + -0.248447205x + x2 = 0 + 2.02484472 Combine like terms: -2.02484472 + 2.02484472 = 0.00000000 0.00000000 + -0.248447205x + x2 = 0 + 2.02484472 -0.248447205x + x2 = 0 + 2.02484472 Combine like terms: 0 + 2.02484472 = 2.02484472 -0.248447205x + x2 = 2.02484472 The x term is -0.248447205x. Take half its coefficient (-0.1242236025). Square it (0.01543150342) and add it to both sides. Add '0.01543150342' to each side of the equation. -0.248447205x + 0.01543150342 + x2 = 2.02484472 + 0.01543150342 Reorder the terms: 0.01543150342 + -0.248447205x + x2 = 2.02484472 + 0.01543150342 Combine like terms: 2.02484472 + 0.01543150342 = 2.04027622342 0.01543150342 + -0.248447205x + x2 = 2.04027622342 Factor a perfect square on the left side: (x + -0.1242236025)(x + -0.1242236025) = 2.04027622342 Calculate the square root of the right side: 1.42838238 Break this problem into two subproblems by setting (x + -0.1242236025) equal to 1.42838238 and -1.42838238.Subproblem 1
x + -0.1242236025 = 1.42838238 Simplifying x + -0.1242236025 = 1.42838238 Reorder the terms: -0.1242236025 + x = 1.42838238 Solving -0.1242236025 + x = 1.42838238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1242236025' to each side of the equation. -0.1242236025 + 0.1242236025 + x = 1.42838238 + 0.1242236025 Combine like terms: -0.1242236025 + 0.1242236025 = 0.0000000000 0.0000000000 + x = 1.42838238 + 0.1242236025 x = 1.42838238 + 0.1242236025 Combine like terms: 1.42838238 + 0.1242236025 = 1.5526059825 x = 1.5526059825 Simplifying x = 1.5526059825Subproblem 2
x + -0.1242236025 = -1.42838238 Simplifying x + -0.1242236025 = -1.42838238 Reorder the terms: -0.1242236025 + x = -1.42838238 Solving -0.1242236025 + x = -1.42838238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1242236025' to each side of the equation. -0.1242236025 + 0.1242236025 + x = -1.42838238 + 0.1242236025 Combine like terms: -0.1242236025 + 0.1242236025 = 0.0000000000 0.0000000000 + x = -1.42838238 + 0.1242236025 x = -1.42838238 + 0.1242236025 Combine like terms: -1.42838238 + 0.1242236025 = -1.3041587775 x = -1.3041587775 Simplifying x = -1.3041587775Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5526059825, -1.3041587775}
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