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Simplifying 7x2 + -5x + -13 = 0 Reorder the terms: -13 + -5x + 7x2 = 0 Solving -13 + -5x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + -0.7142857143x + 1.857142857 + x2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + -0.7142857143x + x2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + 1.857142857 -0.7142857143x + x2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 -0.7142857143x + x2 = 1.857142857 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 1.857142857 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 1.857142857 + 0.1275510204 Combine like terms: 1.857142857 + 0.1275510204 = 1.9846938774 0.1275510204 + -0.7142857143x + x2 = 1.9846938774 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 1.9846938774 Calculate the square root of the right side: 1.408791637 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.408791637 and -1.408791637.Subproblem 1
x + -0.3571428572 = 1.408791637 Simplifying x + -0.3571428572 = 1.408791637 Reorder the terms: -0.3571428572 + x = 1.408791637 Solving -0.3571428572 + x = 1.408791637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.408791637 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.408791637 + 0.3571428572 x = 1.408791637 + 0.3571428572 Combine like terms: 1.408791637 + 0.3571428572 = 1.7659344942 x = 1.7659344942 Simplifying x = 1.7659344942Subproblem 2
x + -0.3571428572 = -1.408791637 Simplifying x + -0.3571428572 = -1.408791637 Reorder the terms: -0.3571428572 + x = -1.408791637 Solving -0.3571428572 + x = -1.408791637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.408791637 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.408791637 + 0.3571428572 x = -1.408791637 + 0.3571428572 Combine like terms: -1.408791637 + 0.3571428572 = -1.0516487798 x = -1.0516487798 Simplifying x = -1.0516487798Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7659344942, -1.0516487798}
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