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Simplifying 1.89 + -0.63x + -0.63x2 = x2 Solving 1.89 + -0.63x + -0.63x2 = x2 Solving for variable 'x'. Combine like terms: -0.63x2 + -1x2 = -1.63x2 1.89 + -0.63x + -1.63x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1.89 + -0.63x + -1.63x2 = 0 Begin completing the square. Divide all terms by -1.63 the coefficient of the squared term: Divide each side by '-1.63'. -1.159509202 + 0.3865030675x + x2 = 0 Move the constant term to the right: Add '1.159509202' to each side of the equation. -1.159509202 + 0.3865030675x + 1.159509202 + x2 = 0 + 1.159509202 Reorder the terms: -1.159509202 + 1.159509202 + 0.3865030675x + x2 = 0 + 1.159509202 Combine like terms: -1.159509202 + 1.159509202 = 0.000000000 0.000000000 + 0.3865030675x + x2 = 0 + 1.159509202 0.3865030675x + x2 = 0 + 1.159509202 Combine like terms: 0 + 1.159509202 = 1.159509202 0.3865030675x + x2 = 1.159509202 The x term is 0.3865030675x. Take half its coefficient (0.1932515338). Square it (0.03734615532) and add it to both sides. Add '0.03734615532' to each side of the equation. 0.3865030675x + 0.03734615532 + x2 = 1.159509202 + 0.03734615532 Reorder the terms: 0.03734615532 + 0.3865030675x + x2 = 1.159509202 + 0.03734615532 Combine like terms: 1.159509202 + 0.03734615532 = 1.19685535732 0.03734615532 + 0.3865030675x + x2 = 1.19685535732 Factor a perfect square on the left side: (x + 0.1932515338)(x + 0.1932515338) = 1.19685535732 Calculate the square root of the right side: 1.094008847 Break this problem into two subproblems by setting (x + 0.1932515338) equal to 1.094008847 and -1.094008847.Subproblem 1
x + 0.1932515338 = 1.094008847 Simplifying x + 0.1932515338 = 1.094008847 Reorder the terms: 0.1932515338 + x = 1.094008847 Solving 0.1932515338 + x = 1.094008847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1932515338' to each side of the equation. 0.1932515338 + -0.1932515338 + x = 1.094008847 + -0.1932515338 Combine like terms: 0.1932515338 + -0.1932515338 = 0.0000000000 0.0000000000 + x = 1.094008847 + -0.1932515338 x = 1.094008847 + -0.1932515338 Combine like terms: 1.094008847 + -0.1932515338 = 0.9007573132 x = 0.9007573132 Simplifying x = 0.9007573132Subproblem 2
x + 0.1932515338 = -1.094008847 Simplifying x + 0.1932515338 = -1.094008847 Reorder the terms: 0.1932515338 + x = -1.094008847 Solving 0.1932515338 + x = -1.094008847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1932515338' to each side of the equation. 0.1932515338 + -0.1932515338 + x = -1.094008847 + -0.1932515338 Combine like terms: 0.1932515338 + -0.1932515338 = 0.0000000000 0.0000000000 + x = -1.094008847 + -0.1932515338 x = -1.094008847 + -0.1932515338 Combine like terms: -1.094008847 + -0.1932515338 = -1.2872603808 x = -1.2872603808 Simplifying x = -1.2872603808Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9007573132, -1.2872603808}
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