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Simplifying 21x2 + -18x + -20 = 0 Reorder the terms: -20 + -18x + 21x2 = 0 Solving -20 + -18x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.9523809524 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.9523809524' to each side of the equation. -0.9523809524 + -0.8571428571x + 0.9523809524 + x2 = 0 + 0.9523809524 Reorder the terms: -0.9523809524 + 0.9523809524 + -0.8571428571x + x2 = 0 + 0.9523809524 Combine like terms: -0.9523809524 + 0.9523809524 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + 0.9523809524 -0.8571428571x + x2 = 0 + 0.9523809524 Combine like terms: 0 + 0.9523809524 = 0.9523809524 -0.8571428571x + x2 = 0.9523809524 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 0.9523809524 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 0.9523809524 + 0.1836734694 Combine like terms: 0.9523809524 + 0.1836734694 = 1.1360544218 0.1836734694 + -0.8571428571x + x2 = 1.1360544218 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 1.1360544218 Calculate the square root of the right side: 1.065858537 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 1.065858537 and -1.065858537.Subproblem 1
x + -0.4285714286 = 1.065858537 Simplifying x + -0.4285714286 = 1.065858537 Reorder the terms: -0.4285714286 + x = 1.065858537 Solving -0.4285714286 + x = 1.065858537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 1.065858537 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.065858537 + 0.4285714286 x = 1.065858537 + 0.4285714286 Combine like terms: 1.065858537 + 0.4285714286 = 1.4944299656 x = 1.4944299656 Simplifying x = 1.4944299656Subproblem 2
x + -0.4285714286 = -1.065858537 Simplifying x + -0.4285714286 = -1.065858537 Reorder the terms: -0.4285714286 + x = -1.065858537 Solving -0.4285714286 + x = -1.065858537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -1.065858537 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.065858537 + 0.4285714286 x = -1.065858537 + 0.4285714286 Combine like terms: -1.065858537 + 0.4285714286 = -0.6372871084 x = -0.6372871084 Simplifying x = -0.6372871084Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4944299656, -0.6372871084}
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