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Simplifying 78x2 + -73x + 4 = 0 Reorder the terms: 4 + -73x + 78x2 = 0 Solving 4 + -73x + 78x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 78 the coefficient of the squared term: Divide each side by '78'. 0.05128205128 + -0.9358974359x + x2 = 0 Move the constant term to the right: Add '-0.05128205128' to each side of the equation. 0.05128205128 + -0.9358974359x + -0.05128205128 + x2 = 0 + -0.05128205128 Reorder the terms: 0.05128205128 + -0.05128205128 + -0.9358974359x + x2 = 0 + -0.05128205128 Combine like terms: 0.05128205128 + -0.05128205128 = 0.00000000000 0.00000000000 + -0.9358974359x + x2 = 0 + -0.05128205128 -0.9358974359x + x2 = 0 + -0.05128205128 Combine like terms: 0 + -0.05128205128 = -0.05128205128 -0.9358974359x + x2 = -0.05128205128 The x term is -0.9358974359x. Take half its coefficient (-0.467948718). Square it (0.2189760027) and add it to both sides. Add '0.2189760027' to each side of the equation. -0.9358974359x + 0.2189760027 + x2 = -0.05128205128 + 0.2189760027 Reorder the terms: 0.2189760027 + -0.9358974359x + x2 = -0.05128205128 + 0.2189760027 Combine like terms: -0.05128205128 + 0.2189760027 = 0.16769395142 0.2189760027 + -0.9358974359x + x2 = 0.16769395142 Factor a perfect square on the left side: (x + -0.467948718)(x + -0.467948718) = 0.16769395142 Calculate the square root of the right side: 0.409504519 Break this problem into two subproblems by setting (x + -0.467948718) equal to 0.409504519 and -0.409504519.Subproblem 1
x + -0.467948718 = 0.409504519 Simplifying x + -0.467948718 = 0.409504519 Reorder the terms: -0.467948718 + x = 0.409504519 Solving -0.467948718 + x = 0.409504519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.467948718' to each side of the equation. -0.467948718 + 0.467948718 + x = 0.409504519 + 0.467948718 Combine like terms: -0.467948718 + 0.467948718 = 0.000000000 0.000000000 + x = 0.409504519 + 0.467948718 x = 0.409504519 + 0.467948718 Combine like terms: 0.409504519 + 0.467948718 = 0.877453237 x = 0.877453237 Simplifying x = 0.877453237Subproblem 2
x + -0.467948718 = -0.409504519 Simplifying x + -0.467948718 = -0.409504519 Reorder the terms: -0.467948718 + x = -0.409504519 Solving -0.467948718 + x = -0.409504519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.467948718' to each side of the equation. -0.467948718 + 0.467948718 + x = -0.409504519 + 0.467948718 Combine like terms: -0.467948718 + 0.467948718 = 0.000000000 0.000000000 + x = -0.409504519 + 0.467948718 x = -0.409504519 + 0.467948718 Combine like terms: -0.409504519 + 0.467948718 = 0.058444199 x = 0.058444199 Simplifying x = 0.058444199Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.877453237, 0.058444199}
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