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Simplifying 25x2 + 70x + 49 = 18 Reorder the terms: 49 + 70x + 25x2 = 18 Solving 49 + 70x + 25x2 = 18 Solving for variable 'x'. Reorder the terms: 49 + -18 + 70x + 25x2 = 18 + -18 Combine like terms: 49 + -18 = 31 31 + 70x + 25x2 = 18 + -18 Combine like terms: 18 + -18 = 0 31 + 70x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.24 + 2.8x + x2 = 0 Move the constant term to the right: Add '-1.24' to each side of the equation. 1.24 + 2.8x + -1.24 + x2 = 0 + -1.24 Reorder the terms: 1.24 + -1.24 + 2.8x + x2 = 0 + -1.24 Combine like terms: 1.24 + -1.24 = 0.00 0.00 + 2.8x + x2 = 0 + -1.24 2.8x + x2 = 0 + -1.24 Combine like terms: 0 + -1.24 = -1.24 2.8x + x2 = -1.24 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = -1.24 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = -1.24 + 1.96 Combine like terms: -1.24 + 1.96 = 0.72 1.96 + 2.8x + x2 = 0.72 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 0.72 Calculate the square root of the right side: 0.848528137 Break this problem into two subproblems by setting (x + 1.4) equal to 0.848528137 and -0.848528137.Subproblem 1
x + 1.4 = 0.848528137 Simplifying x + 1.4 = 0.848528137 Reorder the terms: 1.4 + x = 0.848528137 Solving 1.4 + x = 0.848528137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 0.848528137 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 0.848528137 + -1.4 x = 0.848528137 + -1.4 Combine like terms: 0.848528137 + -1.4 = -0.551471863 x = -0.551471863 Simplifying x = -0.551471863Subproblem 2
x + 1.4 = -0.848528137 Simplifying x + 1.4 = -0.848528137 Reorder the terms: 1.4 + x = -0.848528137 Solving 1.4 + x = -0.848528137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -0.848528137 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -0.848528137 + -1.4 x = -0.848528137 + -1.4 Combine like terms: -0.848528137 + -1.4 = -2.248528137 x = -2.248528137 Simplifying x = -2.248528137Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.551471863, -2.248528137}
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