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Simplifying 8 + -3x(2 + -6x) + -4(5x + 1) = 0 8 + (2 * -3x + -6x * -3x) + -4(5x + 1) = 0 8 + (-6x + 18x2) + -4(5x + 1) = 0 Reorder the terms: 8 + -6x + 18x2 + -4(1 + 5x) = 0 8 + -6x + 18x2 + (1 * -4 + 5x * -4) = 0 8 + -6x + 18x2 + (-4 + -20x) = 0 Reorder the terms: 8 + -4 + -6x + -20x + 18x2 = 0 Combine like terms: 8 + -4 = 4 4 + -6x + -20x + 18x2 = 0 Combine like terms: -6x + -20x = -26x 4 + -26x + 18x2 = 0 Solving 4 + -26x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -13x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -13x + 9x2)' equal to zero and attempt to solve: Simplifying 2 + -13x + 9x2 = 0 Solving 2 + -13x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + -1.444444444x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -1.444444444x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -1.444444444x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -1.444444444x + x2 = 0 + -0.2222222222 -1.444444444x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -1.444444444x + x2 = -0.2222222222 The x term is -1.444444444x. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444x + 0.5216049380 + x2 = -0.2222222222 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444x + x2 = -0.2222222222 + 0.5216049380 Combine like terms: -0.2222222222 + 0.5216049380 = 0.2993827158 0.5216049380 + -1.444444444x + x2 = 0.2993827158 Factor a perfect square on the left side: (x + -0.722222222)(x + -0.722222222) = 0.2993827158 Calculate the square root of the right side: 0.547158767 Break this problem into two subproblems by setting (x + -0.722222222) equal to 0.547158767 and -0.547158767.Subproblem 1
x + -0.722222222 = 0.547158767 Simplifying x + -0.722222222 = 0.547158767 Reorder the terms: -0.722222222 + x = 0.547158767 Solving -0.722222222 + x = 0.547158767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = 0.547158767 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = 0.547158767 + 0.722222222 x = 0.547158767 + 0.722222222 Combine like terms: 0.547158767 + 0.722222222 = 1.269380989 x = 1.269380989 Simplifying x = 1.269380989Subproblem 2
x + -0.722222222 = -0.547158767 Simplifying x + -0.722222222 = -0.547158767 Reorder the terms: -0.722222222 + x = -0.547158767 Solving -0.722222222 + x = -0.547158767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = -0.547158767 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = -0.547158767 + 0.722222222 x = -0.547158767 + 0.722222222 Combine like terms: -0.547158767 + 0.722222222 = 0.175063455 x = 0.175063455 Simplifying x = 0.175063455Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.269380989, 0.175063455}Solution
x = {1.269380989, 0.175063455}
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