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Simplifying x2 + -1.9x + 0.52 = 0 Reorder the terms: 0.52 + -1.9x + x2 = 0 Solving 0.52 + -1.9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.52' to each side of the equation. 0.52 + -1.9x + -0.52 + x2 = 0 + -0.52 Reorder the terms: 0.52 + -0.52 + -1.9x + x2 = 0 + -0.52 Combine like terms: 0.52 + -0.52 = 0.00 0.00 + -1.9x + x2 = 0 + -0.52 -1.9x + x2 = 0 + -0.52 Combine like terms: 0 + -0.52 = -0.52 -1.9x + x2 = -0.52 The x term is -1.9x. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9x + 0.9025 + x2 = -0.52 + 0.9025 Reorder the terms: 0.9025 + -1.9x + x2 = -0.52 + 0.9025 Combine like terms: -0.52 + 0.9025 = 0.3825 0.9025 + -1.9x + x2 = 0.3825 Factor a perfect square on the left side: (x + -0.95)(x + -0.95) = 0.3825 Calculate the square root of the right side: 0.618465844 Break this problem into two subproblems by setting (x + -0.95) equal to 0.618465844 and -0.618465844.Subproblem 1
x + -0.95 = 0.618465844 Simplifying x + -0.95 = 0.618465844 Reorder the terms: -0.95 + x = 0.618465844 Solving -0.95 + x = 0.618465844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 0.618465844 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 0.618465844 + 0.95 x = 0.618465844 + 0.95 Combine like terms: 0.618465844 + 0.95 = 1.568465844 x = 1.568465844 Simplifying x = 1.568465844Subproblem 2
x + -0.95 = -0.618465844 Simplifying x + -0.95 = -0.618465844 Reorder the terms: -0.95 + x = -0.618465844 Solving -0.95 + x = -0.618465844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = -0.618465844 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = -0.618465844 + 0.95 x = -0.618465844 + 0.95 Combine like terms: -0.618465844 + 0.95 = 0.331534156 x = 0.331534156 Simplifying x = 0.331534156Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.568465844, 0.331534156}
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