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Simplifying 13x2 + 7x + -10 = 0 Reorder the terms: -10 + 7x + 13x2 = 0 Solving -10 + 7x + 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'. -0.7692307692 + 0.5384615385x + x2 = 0 Move the constant term to the right: Add '0.7692307692' to each side of the equation. -0.7692307692 + 0.5384615385x + 0.7692307692 + x2 = 0 + 0.7692307692 Reorder the terms: -0.7692307692 + 0.7692307692 + 0.5384615385x + x2 = 0 + 0.7692307692 Combine like terms: -0.7692307692 + 0.7692307692 = 0.0000000000 0.0000000000 + 0.5384615385x + x2 = 0 + 0.7692307692 0.5384615385x + x2 = 0 + 0.7692307692 Combine like terms: 0 + 0.7692307692 = 0.7692307692 0.5384615385x + x2 = 0.7692307692 The x term is 0.5384615385x. Take half its coefficient (0.2692307693). Square it (0.07248520714) and add it to both sides. Add '0.07248520714' to each side of the equation. 0.5384615385x + 0.07248520714 + x2 = 0.7692307692 + 0.07248520714 Reorder the terms: 0.07248520714 + 0.5384615385x + x2 = 0.7692307692 + 0.07248520714 Combine like terms: 0.7692307692 + 0.07248520714 = 0.84171597634 0.07248520714 + 0.5384615385x + x2 = 0.84171597634 Factor a perfect square on the left side: (x + 0.2692307693)(x + 0.2692307693) = 0.84171597634 Calculate the square root of the right side: 0.917450803 Break this problem into two subproblems by setting (x + 0.2692307693) equal to 0.917450803 and -0.917450803.Subproblem 1
x + 0.2692307693 = 0.917450803 Simplifying x + 0.2692307693 = 0.917450803 Reorder the terms: 0.2692307693 + x = 0.917450803 Solving 0.2692307693 + x = 0.917450803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = 0.917450803 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = 0.917450803 + -0.2692307693 x = 0.917450803 + -0.2692307693 Combine like terms: 0.917450803 + -0.2692307693 = 0.6482200337 x = 0.6482200337 Simplifying x = 0.6482200337Subproblem 2
x + 0.2692307693 = -0.917450803 Simplifying x + 0.2692307693 = -0.917450803 Reorder the terms: 0.2692307693 + x = -0.917450803 Solving 0.2692307693 + x = -0.917450803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = -0.917450803 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = -0.917450803 + -0.2692307693 x = -0.917450803 + -0.2692307693 Combine like terms: -0.917450803 + -0.2692307693 = -1.1866815723 x = -1.1866815723 Simplifying x = -1.1866815723Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6482200337, -1.1866815723}
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