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Simplifying 45x2 + 38x + -8 = 0 Reorder the terms: -8 + 38x + 45x2 = 0 Solving -8 + 38x + 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'. -0.1777777778 + 0.8444444444x + x2 = 0 Move the constant term to the right: Add '0.1777777778' to each side of the equation. -0.1777777778 + 0.8444444444x + 0.1777777778 + x2 = 0 + 0.1777777778 Reorder the terms: -0.1777777778 + 0.1777777778 + 0.8444444444x + x2 = 0 + 0.1777777778 Combine like terms: -0.1777777778 + 0.1777777778 = 0.0000000000 0.0000000000 + 0.8444444444x + x2 = 0 + 0.1777777778 0.8444444444x + x2 = 0 + 0.1777777778 Combine like terms: 0 + 0.1777777778 = 0.1777777778 0.8444444444x + x2 = 0.1777777778 The x term is 0.8444444444x. Take half its coefficient (0.4222222222). Square it (0.1782716049) and add it to both sides. Add '0.1782716049' to each side of the equation. 0.8444444444x + 0.1782716049 + x2 = 0.1777777778 + 0.1782716049 Reorder the terms: 0.1782716049 + 0.8444444444x + x2 = 0.1777777778 + 0.1782716049 Combine like terms: 0.1777777778 + 0.1782716049 = 0.3560493827 0.1782716049 + 0.8444444444x + x2 = 0.3560493827 Factor a perfect square on the left side: (x + 0.4222222222)(x + 0.4222222222) = 0.3560493827 Calculate the square root of the right side: 0.596698737 Break this problem into two subproblems by setting (x + 0.4222222222) equal to 0.596698737 and -0.596698737.Subproblem 1
x + 0.4222222222 = 0.596698737 Simplifying x + 0.4222222222 = 0.596698737 Reorder the terms: 0.4222222222 + x = 0.596698737 Solving 0.4222222222 + x = 0.596698737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4222222222' to each side of the equation. 0.4222222222 + -0.4222222222 + x = 0.596698737 + -0.4222222222 Combine like terms: 0.4222222222 + -0.4222222222 = 0.0000000000 0.0000000000 + x = 0.596698737 + -0.4222222222 x = 0.596698737 + -0.4222222222 Combine like terms: 0.596698737 + -0.4222222222 = 0.1744765148 x = 0.1744765148 Simplifying x = 0.1744765148Subproblem 2
x + 0.4222222222 = -0.596698737 Simplifying x + 0.4222222222 = -0.596698737 Reorder the terms: 0.4222222222 + x = -0.596698737 Solving 0.4222222222 + x = -0.596698737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4222222222' to each side of the equation. 0.4222222222 + -0.4222222222 + x = -0.596698737 + -0.4222222222 Combine like terms: 0.4222222222 + -0.4222222222 = 0.0000000000 0.0000000000 + x = -0.596698737 + -0.4222222222 x = -0.596698737 + -0.4222222222 Combine like terms: -0.596698737 + -0.4222222222 = -1.0189209592 x = -1.0189209592 Simplifying x = -1.0189209592Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1744765148, -1.0189209592}
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