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Simplifying 20x2 + 11x + -30 = 0 Reorder the terms: -30 + 11x + 20x2 = 0 Solving -30 + 11x + 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'. -1.5 + 0.55x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.55x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.55x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.55x + x2 = 0 + 1.5 0.55x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 0.55x + x2 = 1.5 The x term is 0.55x. Take half its coefficient (0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. 0.55x + 0.075625 + x2 = 1.5 + 0.075625 Reorder the terms: 0.075625 + 0.55x + x2 = 1.5 + 0.075625 Combine like terms: 1.5 + 0.075625 = 1.575625 0.075625 + 0.55x + x2 = 1.575625 Factor a perfect square on the left side: (x + 0.275)(x + 0.275) = 1.575625 Calculate the square root of the right side: 1.255239021 Break this problem into two subproblems by setting (x + 0.275) equal to 1.255239021 and -1.255239021.Subproblem 1
x + 0.275 = 1.255239021 Simplifying x + 0.275 = 1.255239021 Reorder the terms: 0.275 + x = 1.255239021 Solving 0.275 + x = 1.255239021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + x = 1.255239021 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = 1.255239021 + -0.275 x = 1.255239021 + -0.275 Combine like terms: 1.255239021 + -0.275 = 0.980239021 x = 0.980239021 Simplifying x = 0.980239021Subproblem 2
x + 0.275 = -1.255239021 Simplifying x + 0.275 = -1.255239021 Reorder the terms: 0.275 + x = -1.255239021 Solving 0.275 + x = -1.255239021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + x = -1.255239021 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = -1.255239021 + -0.275 x = -1.255239021 + -0.275 Combine like terms: -1.255239021 + -0.275 = -1.530239021 x = -1.530239021 Simplifying x = -1.530239021Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.980239021, -1.530239021}
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