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Simplifying -11x2 + 8x + -9x2 + 7 = 0 Reorder the terms: 7 + 8x + -11x2 + -9x2 = 0 Combine like terms: -11x2 + -9x2 = -20x2 7 + 8x + -20x2 = 0 Solving 7 + 8x + -20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.35 + -0.4x + x2 = 0.0 Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + -0.4x + 0.35 + x2 = 0.0 + 0.35 Reorder the terms: -0.35 + 0.35 + -0.4x + x2 = 0.0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + -0.4x + x2 = 0.0 + 0.35 -0.4x + x2 = 0.0 + 0.35 Combine like terms: 0.0 + 0.35 = 0.35 -0.4x + x2 = 0.35 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.35 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.35 + 0.04 Combine like terms: 0.35 + 0.04 = 0.39 0.04 + -0.4x + x2 = 0.39 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.39 Calculate the square root of the right side: 0.6244998 Break this problem into two subproblems by setting (x + -0.2) equal to 0.6244998 and -0.6244998.Subproblem 1
x + -0.2 = 0.6244998 Simplifying x + -0.2 = 0.6244998 Reorder the terms: -0.2 + x = 0.6244998 Solving -0.2 + x = 0.6244998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.6244998 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.6244998 + 0.2 x = 0.6244998 + 0.2 Combine like terms: 0.6244998 + 0.2 = 0.8244998 x = 0.8244998 Simplifying x = 0.8244998Subproblem 2
x + -0.2 = -0.6244998 Simplifying x + -0.2 = -0.6244998 Reorder the terms: -0.2 + x = -0.6244998 Solving -0.2 + x = -0.6244998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.6244998 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.6244998 + 0.2 x = -0.6244998 + 0.2 Combine like terms: -0.6244998 + 0.2 = -0.4244998 x = -0.4244998 Simplifying x = -0.4244998Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8244998, -0.4244998}
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