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Simplifying 0.461 = 1.328x + x2 Solving 0.461 = 1.328x + x2 Solving for variable 'x'. Reorder the terms: 0.461 + -1.328x + -1x2 = 1.328x + -1.328x + x2 + -1x2 Combine like terms: 1.328x + -1.328x = 0.000 0.461 + -1.328x + -1x2 = 0.000 + x2 + -1x2 0.461 + -1.328x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.461 + -1.328x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.461 + 1.328x + x2 = 0 Move the constant term to the right: Add '0.461' to each side of the equation. -0.461 + 1.328x + 0.461 + x2 = 0 + 0.461 Reorder the terms: -0.461 + 0.461 + 1.328x + x2 = 0 + 0.461 Combine like terms: -0.461 + 0.461 = 0.000 0.000 + 1.328x + x2 = 0 + 0.461 1.328x + x2 = 0 + 0.461 Combine like terms: 0 + 0.461 = 0.461 1.328x + x2 = 0.461 The x term is 1.328x. Take half its coefficient (0.664). Square it (0.440896) and add it to both sides. Add '0.440896' to each side of the equation. 1.328x + 0.440896 + x2 = 0.461 + 0.440896 Reorder the terms: 0.440896 + 1.328x + x2 = 0.461 + 0.440896 Combine like terms: 0.461 + 0.440896 = 0.901896 0.440896 + 1.328x + x2 = 0.901896 Factor a perfect square on the left side: (x + 0.664)(x + 0.664) = 0.901896 Calculate the square root of the right side: 0.949682052 Break this problem into two subproblems by setting (x + 0.664) equal to 0.949682052 and -0.949682052.Subproblem 1
x + 0.664 = 0.949682052 Simplifying x + 0.664 = 0.949682052 Reorder the terms: 0.664 + x = 0.949682052 Solving 0.664 + x = 0.949682052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.664' to each side of the equation. 0.664 + -0.664 + x = 0.949682052 + -0.664 Combine like terms: 0.664 + -0.664 = 0.000 0.000 + x = 0.949682052 + -0.664 x = 0.949682052 + -0.664 Combine like terms: 0.949682052 + -0.664 = 0.285682052 x = 0.285682052 Simplifying x = 0.285682052Subproblem 2
x + 0.664 = -0.949682052 Simplifying x + 0.664 = -0.949682052 Reorder the terms: 0.664 + x = -0.949682052 Solving 0.664 + x = -0.949682052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.664' to each side of the equation. 0.664 + -0.664 + x = -0.949682052 + -0.664 Combine like terms: 0.664 + -0.664 = 0.000 0.000 + x = -0.949682052 + -0.664 x = -0.949682052 + -0.664 Combine like terms: -0.949682052 + -0.664 = -1.613682052 x = -1.613682052 Simplifying x = -1.613682052Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.285682052, -1.613682052}
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