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Simplifying 5x2 + 40x + 16 = 349 Reorder the terms: 16 + 40x + 5x2 = 349 Solving 16 + 40x + 5x2 = 349 Solving for variable 'x'. Reorder the terms: 16 + -349 + 40x + 5x2 = 349 + -349 Combine like terms: 16 + -349 = -333 -333 + 40x + 5x2 = 349 + -349 Combine like terms: 349 + -349 = 0 -333 + 40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -66.6 + 8x + x2 = 0 Move the constant term to the right: Add '66.6' to each side of the equation. -66.6 + 8x + 66.6 + x2 = 0 + 66.6 Reorder the terms: -66.6 + 66.6 + 8x + x2 = 0 + 66.6 Combine like terms: -66.6 + 66.6 = 0.0 0.0 + 8x + x2 = 0 + 66.6 8x + x2 = 0 + 66.6 Combine like terms: 0 + 66.6 = 66.6 8x + x2 = 66.6 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 66.6 + 16 Reorder the terms: 16 + 8x + x2 = 66.6 + 16 Combine like terms: 66.6 + 16 = 82.6 16 + 8x + x2 = 82.6 Factor a perfect square on the left side: (x + 4)(x + 4) = 82.6 Calculate the square root of the right side: 9.088454214 Break this problem into two subproblems by setting (x + 4) equal to 9.088454214 and -9.088454214.Subproblem 1
x + 4 = 9.088454214 Simplifying x + 4 = 9.088454214 Reorder the terms: 4 + x = 9.088454214 Solving 4 + x = 9.088454214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 9.088454214 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.088454214 + -4 x = 9.088454214 + -4 Combine like terms: 9.088454214 + -4 = 5.088454214 x = 5.088454214 Simplifying x = 5.088454214Subproblem 2
x + 4 = -9.088454214 Simplifying x + 4 = -9.088454214 Reorder the terms: 4 + x = -9.088454214 Solving 4 + x = -9.088454214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -9.088454214 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.088454214 + -4 x = -9.088454214 + -4 Combine like terms: -9.088454214 + -4 = -13.088454214 x = -13.088454214 Simplifying x = -13.088454214Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.088454214, -13.088454214}
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