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Simplifying 13x2 + -21x + -8 = 0 Reorder the terms: -8 + -21x + 13x2 = 0 Solving -8 + -21x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.6153846154 + -1.615384615x + x2 = 0 Move the constant term to the right: Add '0.6153846154' to each side of the equation. -0.6153846154 + -1.615384615x + 0.6153846154 + x2 = 0 + 0.6153846154 Reorder the terms: -0.6153846154 + 0.6153846154 + -1.615384615x + x2 = 0 + 0.6153846154 Combine like terms: -0.6153846154 + 0.6153846154 = 0.0000000000 0.0000000000 + -1.615384615x + x2 = 0 + 0.6153846154 -1.615384615x + x2 = 0 + 0.6153846154 Combine like terms: 0 + 0.6153846154 = 0.6153846154 -1.615384615x + x2 = 0.6153846154 The x term is -1.615384615x. Take half its coefficient (-0.8076923075). Square it (0.6523668636) and add it to both sides. Add '0.6523668636' to each side of the equation. -1.615384615x + 0.6523668636 + x2 = 0.6153846154 + 0.6523668636 Reorder the terms: 0.6523668636 + -1.615384615x + x2 = 0.6153846154 + 0.6523668636 Combine like terms: 0.6153846154 + 0.6523668636 = 1.267751479 0.6523668636 + -1.615384615x + x2 = 1.267751479 Factor a perfect square on the left side: (x + -0.8076923075)(x + -0.8076923075) = 1.267751479 Calculate the square root of the right side: 1.125944705 Break this problem into two subproblems by setting (x + -0.8076923075) equal to 1.125944705 and -1.125944705.Subproblem 1
x + -0.8076923075 = 1.125944705 Simplifying x + -0.8076923075 = 1.125944705 Reorder the terms: -0.8076923075 + x = 1.125944705 Solving -0.8076923075 + x = 1.125944705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8076923075' to each side of the equation. -0.8076923075 + 0.8076923075 + x = 1.125944705 + 0.8076923075 Combine like terms: -0.8076923075 + 0.8076923075 = 0.0000000000 0.0000000000 + x = 1.125944705 + 0.8076923075 x = 1.125944705 + 0.8076923075 Combine like terms: 1.125944705 + 0.8076923075 = 1.9336370125 x = 1.9336370125 Simplifying x = 1.9336370125Subproblem 2
x + -0.8076923075 = -1.125944705 Simplifying x + -0.8076923075 = -1.125944705 Reorder the terms: -0.8076923075 + x = -1.125944705 Solving -0.8076923075 + x = -1.125944705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8076923075' to each side of the equation. -0.8076923075 + 0.8076923075 + x = -1.125944705 + 0.8076923075 Combine like terms: -0.8076923075 + 0.8076923075 = 0.0000000000 0.0000000000 + x = -1.125944705 + 0.8076923075 x = -1.125944705 + 0.8076923075 Combine like terms: -1.125944705 + 0.8076923075 = -0.3182523975 x = -0.3182523975 Simplifying x = -0.3182523975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9336370125, -0.3182523975}
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