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Simplifying 20x2 + 7x + -9 = 0 Reorder the terms: -9 + 7x + 20x2 = 0 Solving -9 + 7x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.45 + 0.35x + x2 = 0 Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 0.35x + 0.45 + x2 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + 0.35x + x2 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 0.35x + x2 = 0 + 0.45 0.35x + x2 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 0.35x + x2 = 0.45 The x term is 0.35x. Take half its coefficient (0.175). Square it (0.030625) and add it to both sides. Add '0.030625' to each side of the equation. 0.35x + 0.030625 + x2 = 0.45 + 0.030625 Reorder the terms: 0.030625 + 0.35x + x2 = 0.45 + 0.030625 Combine like terms: 0.45 + 0.030625 = 0.480625 0.030625 + 0.35x + x2 = 0.480625 Factor a perfect square on the left side: (x + 0.175)(x + 0.175) = 0.480625 Calculate the square root of the right side: 0.693271231 Break this problem into two subproblems by setting (x + 0.175) equal to 0.693271231 and -0.693271231.Subproblem 1
x + 0.175 = 0.693271231 Simplifying x + 0.175 = 0.693271231 Reorder the terms: 0.175 + x = 0.693271231 Solving 0.175 + x = 0.693271231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = 0.693271231 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = 0.693271231 + -0.175 x = 0.693271231 + -0.175 Combine like terms: 0.693271231 + -0.175 = 0.518271231 x = 0.518271231 Simplifying x = 0.518271231Subproblem 2
x + 0.175 = -0.693271231 Simplifying x + 0.175 = -0.693271231 Reorder the terms: 0.175 + x = -0.693271231 Solving 0.175 + x = -0.693271231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = -0.693271231 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = -0.693271231 + -0.175 x = -0.693271231 + -0.175 Combine like terms: -0.693271231 + -0.175 = -0.868271231 x = -0.868271231 Simplifying x = -0.868271231Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.518271231, -0.868271231}
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