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Simplifying 0.714286x2 + 0.75x + -0.321429 = 0 Reorder the terms: -0.321429 + 0.75x + 0.714286x2 = 0 Solving -0.321429 + 0.75x + 0.714286x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.714286 the coefficient of the squared term: Divide each side by '0.714286'. -0.45000042 + 1.04999958x + x2 = 0 Move the constant term to the right: Add '0.45000042' to each side of the equation. -0.45000042 + 1.04999958x + 0.45000042 + x2 = 0 + 0.45000042 Reorder the terms: -0.45000042 + 0.45000042 + 1.04999958x + x2 = 0 + 0.45000042 Combine like terms: -0.45000042 + 0.45000042 = 0.00000000 0.00000000 + 1.04999958x + x2 = 0 + 0.45000042 1.04999958x + x2 = 0 + 0.45000042 Combine like terms: 0 + 0.45000042 = 0.45000042 1.04999958x + x2 = 0.45000042 The x term is 1.04999958x. Take half its coefficient (0.52499979). Square it (0.2756247795) and add it to both sides. Add '0.2756247795' to each side of the equation. 1.04999958x + 0.2756247795 + x2 = 0.45000042 + 0.2756247795 Reorder the terms: 0.2756247795 + 1.04999958x + x2 = 0.45000042 + 0.2756247795 Combine like terms: 0.45000042 + 0.2756247795 = 0.7256251995 0.2756247795 + 1.04999958x + x2 = 0.7256251995 Factor a perfect square on the left side: (x + 0.52499979)(x + 0.52499979) = 0.7256251995 Calculate the square root of the right side: 0.851836369 Break this problem into two subproblems by setting (x + 0.52499979) equal to 0.851836369 and -0.851836369.Subproblem 1
x + 0.52499979 = 0.851836369 Simplifying x + 0.52499979 = 0.851836369 Reorder the terms: 0.52499979 + x = 0.851836369 Solving 0.52499979 + x = 0.851836369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.52499979' to each side of the equation. 0.52499979 + -0.52499979 + x = 0.851836369 + -0.52499979 Combine like terms: 0.52499979 + -0.52499979 = 0.00000000 0.00000000 + x = 0.851836369 + -0.52499979 x = 0.851836369 + -0.52499979 Combine like terms: 0.851836369 + -0.52499979 = 0.326836579 x = 0.326836579 Simplifying x = 0.326836579Subproblem 2
x + 0.52499979 = -0.851836369 Simplifying x + 0.52499979 = -0.851836369 Reorder the terms: 0.52499979 + x = -0.851836369 Solving 0.52499979 + x = -0.851836369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.52499979' to each side of the equation. 0.52499979 + -0.52499979 + x = -0.851836369 + -0.52499979 Combine like terms: 0.52499979 + -0.52499979 = 0.00000000 0.00000000 + x = -0.851836369 + -0.52499979 x = -0.851836369 + -0.52499979 Combine like terms: -0.851836369 + -0.52499979 = -1.376836159 x = -1.376836159 Simplifying x = -1.376836159Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.326836579, -1.376836159}
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