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Simplifying 13x2 + 8x = 44 Reorder the terms: 8x + 13x2 = 44 Solving 8x + 13x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + 8x + 13x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 8x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -3.384615385 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '3.384615385' to each side of the equation. -3.384615385 + 0.6153846154x + 3.384615385 + x2 = 0 + 3.384615385 Reorder the terms: -3.384615385 + 3.384615385 + 0.6153846154x + x2 = 0 + 3.384615385 Combine like terms: -3.384615385 + 3.384615385 = 0.000000000 0.000000000 + 0.6153846154x + x2 = 0 + 3.384615385 0.6153846154x + x2 = 0 + 3.384615385 Combine like terms: 0 + 3.384615385 = 3.384615385 0.6153846154x + x2 = 3.384615385 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 = 3.384615385 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = 3.384615385 + 0.09467455622 Combine like terms: 3.384615385 + 0.09467455622 = 3.47928994122 0.09467455622 + 0.6153846154x + x2 = 3.47928994122 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = 3.47928994122 Calculate the square root of the right side: 1.865285485 Break this problem into two subproblems by setting (x + 0.3076923077) equal to 1.865285485 and -1.865285485.Subproblem 1
x + 0.3076923077 = 1.865285485 Simplifying x + 0.3076923077 = 1.865285485 Reorder the terms: 0.3076923077 + x = 1.865285485 Solving 0.3076923077 + x = 1.865285485 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 = 1.865285485 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = 1.865285485 + -0.3076923077 x = 1.865285485 + -0.3076923077 Combine like terms: 1.865285485 + -0.3076923077 = 1.5575931773 x = 1.5575931773 Simplifying x = 1.5575931773Subproblem 2
x + 0.3076923077 = -1.865285485 Simplifying x + 0.3076923077 = -1.865285485 Reorder the terms: 0.3076923077 + x = -1.865285485 Solving 0.3076923077 + x = -1.865285485 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 = -1.865285485 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = -1.865285485 + -0.3076923077 x = -1.865285485 + -0.3076923077 Combine like terms: -1.865285485 + -0.3076923077 = -2.1729777927 x = -2.1729777927 Simplifying x = -2.1729777927Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5575931773, -2.1729777927}
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