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Simplifying -9x + -8(5x2 + -5) + 6x2 = 0 Reorder the terms: -9x + -8(-5 + 5x2) + 6x2 = 0 -9x + (-5 * -8 + 5x2 * -8) + 6x2 = 0 -9x + (40 + -40x2) + 6x2 = 0 Reorder the terms: 40 + -9x + -40x2 + 6x2 = 0 Combine like terms: -40x2 + 6x2 = -34x2 40 + -9x + -34x2 = 0 Solving 40 + -9x + -34x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -34 the coefficient of the squared term: Divide each side by '-34'. -1.176470588 + 0.2647058824x + x2 = 0 Move the constant term to the right: Add '1.176470588' to each side of the equation. -1.176470588 + 0.2647058824x + 1.176470588 + x2 = 0 + 1.176470588 Reorder the terms: -1.176470588 + 1.176470588 + 0.2647058824x + x2 = 0 + 1.176470588 Combine like terms: -1.176470588 + 1.176470588 = 0.000000000 0.000000000 + 0.2647058824x + x2 = 0 + 1.176470588 0.2647058824x + x2 = 0 + 1.176470588 Combine like terms: 0 + 1.176470588 = 1.176470588 0.2647058824x + x2 = 1.176470588 The x term is 0.2647058824x. Take half its coefficient (0.1323529412). Square it (0.01751730104) and add it to both sides. Add '0.01751730104' to each side of the equation. 0.2647058824x + 0.01751730104 + x2 = 1.176470588 + 0.01751730104 Reorder the terms: 0.01751730104 + 0.2647058824x + x2 = 1.176470588 + 0.01751730104 Combine like terms: 1.176470588 + 0.01751730104 = 1.19398788904 0.01751730104 + 0.2647058824x + x2 = 1.19398788904 Factor a perfect square on the left side: (x + 0.1323529412)(x + 0.1323529412) = 1.19398788904 Calculate the square root of the right side: 1.092697529 Break this problem into two subproblems by setting (x + 0.1323529412) equal to 1.092697529 and -1.092697529.Subproblem 1
x + 0.1323529412 = 1.092697529 Simplifying x + 0.1323529412 = 1.092697529 Reorder the terms: 0.1323529412 + x = 1.092697529 Solving 0.1323529412 + x = 1.092697529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1323529412' to each side of the equation. 0.1323529412 + -0.1323529412 + x = 1.092697529 + -0.1323529412 Combine like terms: 0.1323529412 + -0.1323529412 = 0.0000000000 0.0000000000 + x = 1.092697529 + -0.1323529412 x = 1.092697529 + -0.1323529412 Combine like terms: 1.092697529 + -0.1323529412 = 0.9603445878 x = 0.9603445878 Simplifying x = 0.9603445878Subproblem 2
x + 0.1323529412 = -1.092697529 Simplifying x + 0.1323529412 = -1.092697529 Reorder the terms: 0.1323529412 + x = -1.092697529 Solving 0.1323529412 + x = -1.092697529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1323529412' to each side of the equation. 0.1323529412 + -0.1323529412 + x = -1.092697529 + -0.1323529412 Combine like terms: 0.1323529412 + -0.1323529412 = 0.0000000000 0.0000000000 + x = -1.092697529 + -0.1323529412 x = -1.092697529 + -0.1323529412 Combine like terms: -1.092697529 + -0.1323529412 = -1.2250504702 x = -1.2250504702 Simplifying x = -1.2250504702Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9603445878, -1.2250504702}
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