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Simplifying (-7x2 + 8x) + -1(9x2 + 11x + -3) = 0 Reorder the terms: (8x + -7x2) + -1(9x2 + 11x + -3) = 0 Remove parenthesis around (8x + -7x2) 8x + -7x2 + -1(9x2 + 11x + -3) = 0 Reorder the terms: 8x + -7x2 + -1(-3 + 11x + 9x2) = 0 8x + -7x2 + (-3 * -1 + 11x * -1 + 9x2 * -1) = 0 8x + -7x2 + (3 + -11x + -9x2) = 0 Reorder the terms: 3 + 8x + -11x + -7x2 + -9x2 = 0 Combine like terms: 8x + -11x = -3x 3 + -3x + -7x2 + -9x2 = 0 Combine like terms: -7x2 + -9x2 = -16x2 3 + -3x + -16x2 = 0 Solving 3 + -3x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.1875 + 0.1875x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 0.1875x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 0.1875x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 0.1875x + x2 = 0 + 0.1875 0.1875x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 0.1875x + x2 = 0.1875 The x term is 0.1875x. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875x + 0.0087890625 + x2 = 0.1875 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 0.1875 + 0.0087890625 Combine like terms: 0.1875 + 0.0087890625 = 0.1962890625 0.0087890625 + 0.1875x + x2 = 0.1962890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 0.1962890625 Calculate the square root of the right side: 0.443045215 Break this problem into two subproblems by setting (x + 0.09375) equal to 0.443045215 and -0.443045215.Subproblem 1
x + 0.09375 = 0.443045215 Simplifying x + 0.09375 = 0.443045215 Reorder the terms: 0.09375 + x = 0.443045215 Solving 0.09375 + x = 0.443045215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = 0.443045215 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 0.443045215 + -0.09375 x = 0.443045215 + -0.09375 Combine like terms: 0.443045215 + -0.09375 = 0.349295215 x = 0.349295215 Simplifying x = 0.349295215Subproblem 2
x + 0.09375 = -0.443045215 Simplifying x + 0.09375 = -0.443045215 Reorder the terms: 0.09375 + x = -0.443045215 Solving 0.09375 + x = -0.443045215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = -0.443045215 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -0.443045215 + -0.09375 x = -0.443045215 + -0.09375 Combine like terms: -0.443045215 + -0.09375 = -0.536795215 x = -0.536795215 Simplifying x = -0.536795215Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.349295215, -0.536795215}
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