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Simplifying 28.2x2 + 3x + -5 = 0 Reorder the terms: -5 + 3x + 28.2x2 = 0 Solving -5 + 3x + 28.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28.2 the coefficient of the squared term: Divide each side by '28.2'. -0.1773049645 + 0.1063829787x + x2 = 0 Move the constant term to the right: Add '0.1773049645' to each side of the equation. -0.1773049645 + 0.1063829787x + 0.1773049645 + x2 = 0 + 0.1773049645 Reorder the terms: -0.1773049645 + 0.1773049645 + 0.1063829787x + x2 = 0 + 0.1773049645 Combine like terms: -0.1773049645 + 0.1773049645 = 0.0000000000 0.0000000000 + 0.1063829787x + x2 = 0 + 0.1773049645 0.1063829787x + x2 = 0 + 0.1773049645 Combine like terms: 0 + 0.1773049645 = 0.1773049645 0.1063829787x + x2 = 0.1773049645 The x term is 0.1063829787x. Take half its coefficient (0.05319148935). Square it (0.002829334539) and add it to both sides. Add '0.002829334539' to each side of the equation. 0.1063829787x + 0.002829334539 + x2 = 0.1773049645 + 0.002829334539 Reorder the terms: 0.002829334539 + 0.1063829787x + x2 = 0.1773049645 + 0.002829334539 Combine like terms: 0.1773049645 + 0.002829334539 = 0.180134299039 0.002829334539 + 0.1063829787x + x2 = 0.180134299039 Factor a perfect square on the left side: (x + 0.05319148935)(x + 0.05319148935) = 0.180134299039 Calculate the square root of the right side: 0.424422312 Break this problem into two subproblems by setting (x + 0.05319148935) equal to 0.424422312 and -0.424422312.Subproblem 1
x + 0.05319148935 = 0.424422312 Simplifying x + 0.05319148935 = 0.424422312 Reorder the terms: 0.05319148935 + x = 0.424422312 Solving 0.05319148935 + x = 0.424422312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05319148935' to each side of the equation. 0.05319148935 + -0.05319148935 + x = 0.424422312 + -0.05319148935 Combine like terms: 0.05319148935 + -0.05319148935 = 0.00000000000 0.00000000000 + x = 0.424422312 + -0.05319148935 x = 0.424422312 + -0.05319148935 Combine like terms: 0.424422312 + -0.05319148935 = 0.37123082265 x = 0.37123082265 Simplifying x = 0.37123082265Subproblem 2
x + 0.05319148935 = -0.424422312 Simplifying x + 0.05319148935 = -0.424422312 Reorder the terms: 0.05319148935 + x = -0.424422312 Solving 0.05319148935 + x = -0.424422312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05319148935' to each side of the equation. 0.05319148935 + -0.05319148935 + x = -0.424422312 + -0.05319148935 Combine like terms: 0.05319148935 + -0.05319148935 = 0.00000000000 0.00000000000 + x = -0.424422312 + -0.05319148935 x = -0.424422312 + -0.05319148935 Combine like terms: -0.424422312 + -0.05319148935 = -0.47761380135 x = -0.47761380135 Simplifying x = -0.47761380135Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.37123082265, -0.47761380135}
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