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Simplifying 4.9x2 + 4x + -23 = 0 Reorder the terms: -23 + 4x + 4.9x2 = 0 Solving -23 + 4x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.693877551 + 0.8163265306x + x2 = 0 Move the constant term to the right: Add '4.693877551' to each side of the equation. -4.693877551 + 0.8163265306x + 4.693877551 + x2 = 0 + 4.693877551 Reorder the terms: -4.693877551 + 4.693877551 + 0.8163265306x + x2 = 0 + 4.693877551 Combine like terms: -4.693877551 + 4.693877551 = 0.000000000 0.000000000 + 0.8163265306x + x2 = 0 + 4.693877551 0.8163265306x + x2 = 0 + 4.693877551 Combine like terms: 0 + 4.693877551 = 4.693877551 0.8163265306x + x2 = 4.693877551 The x term is 0.8163265306x. Take half its coefficient (0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. 0.8163265306x + 0.1665972511 + x2 = 4.693877551 + 0.1665972511 Reorder the terms: 0.1665972511 + 0.8163265306x + x2 = 4.693877551 + 0.1665972511 Combine like terms: 4.693877551 + 0.1665972511 = 4.8604748021 0.1665972511 + 0.8163265306x + x2 = 4.8604748021 Factor a perfect square on the left side: (x + 0.4081632653)(x + 0.4081632653) = 4.8604748021 Calculate the square root of the right side: 2.204648453 Break this problem into two subproblems by setting (x + 0.4081632653) equal to 2.204648453 and -2.204648453.Subproblem 1
x + 0.4081632653 = 2.204648453 Simplifying x + 0.4081632653 = 2.204648453 Reorder the terms: 0.4081632653 + x = 2.204648453 Solving 0.4081632653 + x = 2.204648453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + x = 2.204648453 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + x = 2.204648453 + -0.4081632653 x = 2.204648453 + -0.4081632653 Combine like terms: 2.204648453 + -0.4081632653 = 1.7964851877 x = 1.7964851877 Simplifying x = 1.7964851877Subproblem 2
x + 0.4081632653 = -2.204648453 Simplifying x + 0.4081632653 = -2.204648453 Reorder the terms: 0.4081632653 + x = -2.204648453 Solving 0.4081632653 + x = -2.204648453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + x = -2.204648453 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + x = -2.204648453 + -0.4081632653 x = -2.204648453 + -0.4081632653 Combine like terms: -2.204648453 + -0.4081632653 = -2.6128117183 x = -2.6128117183 Simplifying x = -2.6128117183Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7964851877, -2.6128117183}
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