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Simplifying 49x2 + -7x + -15 = 0 Reorder the terms: -15 + -7x + 49x2 = 0 Solving -15 + -7x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.306122449 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -0.1428571429x + 0.306122449 + x2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -0.1428571429x + x2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 0.306122449 -0.1428571429x + x2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -0.1428571429x + x2 = 0.306122449 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 0.306122449 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 0.306122449 + 0.005102040819 Combine like terms: 0.306122449 + 0.005102040819 = 0.311224489819 0.005102040819 + -0.1428571429x + x2 = 0.311224489819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 0.311224489819 Calculate the square root of the right side: 0.557874977 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 0.557874977 and -0.557874977.Subproblem 1
x + -0.07142857145 = 0.557874977 Simplifying x + -0.07142857145 = 0.557874977 Reorder the terms: -0.07142857145 + x = 0.557874977 Solving -0.07142857145 + x = 0.557874977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.557874977 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.557874977 + 0.07142857145 x = 0.557874977 + 0.07142857145 Combine like terms: 0.557874977 + 0.07142857145 = 0.62930354845 x = 0.62930354845 Simplifying x = 0.62930354845Subproblem 2
x + -0.07142857145 = -0.557874977 Simplifying x + -0.07142857145 = -0.557874977 Reorder the terms: -0.07142857145 + x = -0.557874977 Solving -0.07142857145 + x = -0.557874977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.557874977 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.557874977 + 0.07142857145 x = -0.557874977 + 0.07142857145 Combine like terms: -0.557874977 + 0.07142857145 = -0.48644640555 x = -0.48644640555 Simplifying x = -0.48644640555Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.62930354845, -0.48644640555}
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