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Simplifying 5x2 + 7x = 11 Reorder the terms: 7x + 5x2 = 11 Solving 7x + 5x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 7x + 5x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + 1.4x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 1.4x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 1.4x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 1.4x + x2 = 0 + 2.2 1.4x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 1.4x + x2 = 2.2 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 2.2 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 2.2 + 0.49 Combine like terms: 2.2 + 0.49 = 2.69 0.49 + 1.4x + x2 = 2.69 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 2.69 Calculate the square root of the right side: 1.640121947 Break this problem into two subproblems by setting (x + 0.7) equal to 1.640121947 and -1.640121947.Subproblem 1
x + 0.7 = 1.640121947 Simplifying x + 0.7 = 1.640121947 Reorder the terms: 0.7 + x = 1.640121947 Solving 0.7 + x = 1.640121947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 1.640121947 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 1.640121947 + -0.7 x = 1.640121947 + -0.7 Combine like terms: 1.640121947 + -0.7 = 0.940121947 x = 0.940121947 Simplifying x = 0.940121947Subproblem 2
x + 0.7 = -1.640121947 Simplifying x + 0.7 = -1.640121947 Reorder the terms: 0.7 + x = -1.640121947 Solving 0.7 + x = -1.640121947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -1.640121947 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -1.640121947 + -0.7 x = -1.640121947 + -0.7 Combine like terms: -1.640121947 + -0.7 = -2.340121947 x = -2.340121947 Simplifying x = -2.340121947Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.940121947, -2.340121947}
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