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Simplifying 20x2 + 84x + -49 = 0 Reorder the terms: -49 + 84x + 20x2 = 0 Solving -49 + 84x + 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'. -2.45 + 4.2x + x2 = 0 Move the constant term to the right: Add '2.45' to each side of the equation. -2.45 + 4.2x + 2.45 + x2 = 0 + 2.45 Reorder the terms: -2.45 + 2.45 + 4.2x + x2 = 0 + 2.45 Combine like terms: -2.45 + 2.45 = 0.00 0.00 + 4.2x + x2 = 0 + 2.45 4.2x + x2 = 0 + 2.45 Combine like terms: 0 + 2.45 = 2.45 4.2x + x2 = 2.45 The x term is 4.2x. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2x + 4.41 + x2 = 2.45 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 2.45 + 4.41 Combine like terms: 2.45 + 4.41 = 6.86 4.41 + 4.2x + x2 = 6.86 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 6.86 Calculate the square root of the right side: 2.619160171 Break this problem into two subproblems by setting (x + 2.1) equal to 2.619160171 and -2.619160171.Subproblem 1
x + 2.1 = 2.619160171 Simplifying x + 2.1 = 2.619160171 Reorder the terms: 2.1 + x = 2.619160171 Solving 2.1 + x = 2.619160171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = 2.619160171 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 2.619160171 + -2.1 x = 2.619160171 + -2.1 Combine like terms: 2.619160171 + -2.1 = 0.519160171 x = 0.519160171 Simplifying x = 0.519160171Subproblem 2
x + 2.1 = -2.619160171 Simplifying x + 2.1 = -2.619160171 Reorder the terms: 2.1 + x = -2.619160171 Solving 2.1 + x = -2.619160171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = -2.619160171 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -2.619160171 + -2.1 x = -2.619160171 + -2.1 Combine like terms: -2.619160171 + -2.1 = -4.719160171 x = -4.719160171 Simplifying x = -4.719160171Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.519160171, -4.719160171}
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