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Simplifying 13x2 + -8x + -20 = 0 Reorder the terms: -20 + -8x + 13x2 = 0 Solving -20 + -8x + 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'. -1.538461538 + -0.6153846154x + x2 = 0 Move the constant term to the right: Add '1.538461538' to each side of the equation. -1.538461538 + -0.6153846154x + 1.538461538 + x2 = 0 + 1.538461538 Reorder the terms: -1.538461538 + 1.538461538 + -0.6153846154x + x2 = 0 + 1.538461538 Combine like terms: -1.538461538 + 1.538461538 = 0.000000000 0.000000000 + -0.6153846154x + x2 = 0 + 1.538461538 -0.6153846154x + x2 = 0 + 1.538461538 Combine like terms: 0 + 1.538461538 = 1.538461538 -0.6153846154x + x2 = 1.538461538 The x term is -0.6153846154x. Take half its coefficient (-0.3076923077). Square it (0.09467455622) and add it to both sides. Add '0.09467455622' to each side of the equation. -0.6153846154x + 0.09467455622 + x2 = 1.538461538 + 0.09467455622 Reorder the terms: 0.09467455622 + -0.6153846154x + x2 = 1.538461538 + 0.09467455622 Combine like terms: 1.538461538 + 0.09467455622 = 1.63313609422 0.09467455622 + -0.6153846154x + x2 = 1.63313609422 Factor a perfect square on the left side: (x + -0.3076923077)(x + -0.3076923077) = 1.63313609422 Calculate the square root of the right side: 1.277942133 Break this problem into two subproblems by setting (x + -0.3076923077) equal to 1.277942133 and -1.277942133.Subproblem 1
x + -0.3076923077 = 1.277942133 Simplifying x + -0.3076923077 = 1.277942133 Reorder the terms: -0.3076923077 + x = 1.277942133 Solving -0.3076923077 + x = 1.277942133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + x = 1.277942133 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + x = 1.277942133 + 0.3076923077 x = 1.277942133 + 0.3076923077 Combine like terms: 1.277942133 + 0.3076923077 = 1.5856344407 x = 1.5856344407 Simplifying x = 1.5856344407Subproblem 2
x + -0.3076923077 = -1.277942133 Simplifying x + -0.3076923077 = -1.277942133 Reorder the terms: -0.3076923077 + x = -1.277942133 Solving -0.3076923077 + x = -1.277942133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.3076923077 + x = -1.277942133 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + x = -1.277942133 + 0.3076923077 x = -1.277942133 + 0.3076923077 Combine like terms: -1.277942133 + 0.3076923077 = -0.9702498253 x = -0.9702498253 Simplifying x = -0.9702498253Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5856344407, -0.9702498253}
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