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Simplifying 45x2 + -4x + -5 = 0 Reorder the terms: -5 + -4x + 45x2 = 0 Solving -5 + -4x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.1111111111 + -0.08888888889x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.08888888889x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.08888888889x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.08888888889x + x2 = 0 + 0.1111111111 -0.08888888889x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.08888888889x + x2 = 0.1111111111 The x term is -0.08888888889x. Take half its coefficient (-0.04444444445). Square it (0.001975308642) and add it to both sides. Add '0.001975308642' to each side of the equation. -0.08888888889x + 0.001975308642 + x2 = 0.1111111111 + 0.001975308642 Reorder the terms: 0.001975308642 + -0.08888888889x + x2 = 0.1111111111 + 0.001975308642 Combine like terms: 0.1111111111 + 0.001975308642 = 0.113086419742 0.001975308642 + -0.08888888889x + x2 = 0.113086419742 Factor a perfect square on the left side: (x + -0.04444444445)(x + -0.04444444445) = 0.113086419742 Calculate the square root of the right side: 0.336283243 Break this problem into two subproblems by setting (x + -0.04444444445) equal to 0.336283243 and -0.336283243.Subproblem 1
x + -0.04444444445 = 0.336283243 Simplifying x + -0.04444444445 = 0.336283243 Reorder the terms: -0.04444444445 + x = 0.336283243 Solving -0.04444444445 + x = 0.336283243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04444444445' to each side of the equation. -0.04444444445 + 0.04444444445 + x = 0.336283243 + 0.04444444445 Combine like terms: -0.04444444445 + 0.04444444445 = 0.00000000000 0.00000000000 + x = 0.336283243 + 0.04444444445 x = 0.336283243 + 0.04444444445 Combine like terms: 0.336283243 + 0.04444444445 = 0.38072768745 x = 0.38072768745 Simplifying x = 0.38072768745Subproblem 2
x + -0.04444444445 = -0.336283243 Simplifying x + -0.04444444445 = -0.336283243 Reorder the terms: -0.04444444445 + x = -0.336283243 Solving -0.04444444445 + x = -0.336283243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04444444445' to each side of the equation. -0.04444444445 + 0.04444444445 + x = -0.336283243 + 0.04444444445 Combine like terms: -0.04444444445 + 0.04444444445 = 0.00000000000 0.00000000000 + x = -0.336283243 + 0.04444444445 x = -0.336283243 + 0.04444444445 Combine like terms: -0.336283243 + 0.04444444445 = -0.29183879855 x = -0.29183879855 Simplifying x = -0.29183879855Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.38072768745, -0.29183879855}
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