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Simplifying 0.115 = 0.45x + x2 Solving 0.115 = 0.45x + x2 Solving for variable 'x'. Reorder the terms: 0.115 + -0.45x + -1x2 = 0.45x + -0.45x + x2 + -1x2 Combine like terms: 0.45x + -0.45x = 0.00 0.115 + -0.45x + -1x2 = 0.00 + x2 + -1x2 0.115 + -0.45x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.115 + -0.45x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.115 + 0.45x + x2 = 0 Move the constant term to the right: Add '0.115' to each side of the equation. -0.115 + 0.45x + 0.115 + x2 = 0 + 0.115 Reorder the terms: -0.115 + 0.115 + 0.45x + x2 = 0 + 0.115 Combine like terms: -0.115 + 0.115 = 0.000 0.000 + 0.45x + x2 = 0 + 0.115 0.45x + x2 = 0 + 0.115 Combine like terms: 0 + 0.115 = 0.115 0.45x + x2 = 0.115 The x term is 0.45x. Take half its coefficient (0.225). Square it (0.050625) and add it to both sides. Add '0.050625' to each side of the equation. 0.45x + 0.050625 + x2 = 0.115 + 0.050625 Reorder the terms: 0.050625 + 0.45x + x2 = 0.115 + 0.050625 Combine like terms: 0.115 + 0.050625 = 0.165625 0.050625 + 0.45x + x2 = 0.165625 Factor a perfect square on the left side: (x + 0.225)(x + 0.225) = 0.165625 Calculate the square root of the right side: 0.406970515 Break this problem into two subproblems by setting (x + 0.225) equal to 0.406970515 and -0.406970515.Subproblem 1
x + 0.225 = 0.406970515 Simplifying x + 0.225 = 0.406970515 Reorder the terms: 0.225 + x = 0.406970515 Solving 0.225 + x = 0.406970515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.225' to each side of the equation. 0.225 + -0.225 + x = 0.406970515 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + x = 0.406970515 + -0.225 x = 0.406970515 + -0.225 Combine like terms: 0.406970515 + -0.225 = 0.181970515 x = 0.181970515 Simplifying x = 0.181970515Subproblem 2
x + 0.225 = -0.406970515 Simplifying x + 0.225 = -0.406970515 Reorder the terms: 0.225 + x = -0.406970515 Solving 0.225 + x = -0.406970515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.225' to each side of the equation. 0.225 + -0.225 + x = -0.406970515 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + x = -0.406970515 + -0.225 x = -0.406970515 + -0.225 Combine like terms: -0.406970515 + -0.225 = -0.631970515 x = -0.631970515 Simplifying x = -0.631970515Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.181970515, -0.631970515}
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