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Simplifying 49x2 + -490x = 15 Reorder the terms: -490x + 49x2 = 15 Solving -490x + 49x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -490x + 49x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -490x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.306122449 + -10x + x2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -10x + 0.306122449 + x2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -10x + x2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -10x + x2 = 0 + 0.306122449 -10x + x2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -10x + x2 = 0.306122449 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 0.306122449 + 25 Reorder the terms: 25 + -10x + x2 = 0.306122449 + 25 Combine like terms: 0.306122449 + 25 = 25.306122449 25 + -10x + x2 = 25.306122449 Factor a perfect square on the left side: (x + -5)(x + -5) = 25.306122449 Calculate the square root of the right side: 5.030519103 Break this problem into two subproblems by setting (x + -5) equal to 5.030519103 and -5.030519103.Subproblem 1
x + -5 = 5.030519103 Simplifying x + -5 = 5.030519103 Reorder the terms: -5 + x = 5.030519103 Solving -5 + x = 5.030519103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.030519103 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.030519103 + 5 x = 5.030519103 + 5 Combine like terms: 5.030519103 + 5 = 10.030519103 x = 10.030519103 Simplifying x = 10.030519103Subproblem 2
x + -5 = -5.030519103 Simplifying x + -5 = -5.030519103 Reorder the terms: -5 + x = -5.030519103 Solving -5 + x = -5.030519103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.030519103 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.030519103 + 5 x = -5.030519103 + 5 Combine like terms: -5.030519103 + 5 = -0.030519103 x = -0.030519103 Simplifying x = -0.030519103Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.030519103, -0.030519103}
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