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Simplifying 20x2 + 11x + -3 = 130 Reorder the terms: -3 + 11x + 20x2 = 130 Solving -3 + 11x + 20x2 = 130 Solving for variable 'x'. Reorder the terms: -3 + -130 + 11x + 20x2 = 130 + -130 Combine like terms: -3 + -130 = -133 -133 + 11x + 20x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -133 + 11x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -6.65 + 0.55x + x2 = 0 Move the constant term to the right: Add '6.65' to each side of the equation. -6.65 + 0.55x + 6.65 + x2 = 0 + 6.65 Reorder the terms: -6.65 + 6.65 + 0.55x + x2 = 0 + 6.65 Combine like terms: -6.65 + 6.65 = 0.00 0.00 + 0.55x + x2 = 0 + 6.65 0.55x + x2 = 0 + 6.65 Combine like terms: 0 + 6.65 = 6.65 0.55x + x2 = 6.65 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 = 6.65 + 0.075625 Reorder the terms: 0.075625 + 0.55x + x2 = 6.65 + 0.075625 Combine like terms: 6.65 + 0.075625 = 6.725625 0.075625 + 0.55x + x2 = 6.725625 Factor a perfect square on the left side: (x + 0.275)(x + 0.275) = 6.725625 Calculate the square root of the right side: 2.593380998 Break this problem into two subproblems by setting (x + 0.275) equal to 2.593380998 and -2.593380998.Subproblem 1
x + 0.275 = 2.593380998 Simplifying x + 0.275 = 2.593380998 Reorder the terms: 0.275 + x = 2.593380998 Solving 0.275 + x = 2.593380998 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 = 2.593380998 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = 2.593380998 + -0.275 x = 2.593380998 + -0.275 Combine like terms: 2.593380998 + -0.275 = 2.318380998 x = 2.318380998 Simplifying x = 2.318380998Subproblem 2
x + 0.275 = -2.593380998 Simplifying x + 0.275 = -2.593380998 Reorder the terms: 0.275 + x = -2.593380998 Solving 0.275 + x = -2.593380998 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 = -2.593380998 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = -2.593380998 + -0.275 x = -2.593380998 + -0.275 Combine like terms: -2.593380998 + -0.275 = -2.868380998 x = -2.868380998 Simplifying x = -2.868380998Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.318380998, -2.868380998}
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