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Simplifying 11x2 + 13x = 48 Reorder the terms: 13x + 11x2 = 48 Solving 13x + 11x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + 13x + 11x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 13x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -4.363636364 + 1.181818182x + x2 = 0 Move the constant term to the right: Add '4.363636364' to each side of the equation. -4.363636364 + 1.181818182x + 4.363636364 + x2 = 0 + 4.363636364 Reorder the terms: -4.363636364 + 4.363636364 + 1.181818182x + x2 = 0 + 4.363636364 Combine like terms: -4.363636364 + 4.363636364 = 0.000000000 0.000000000 + 1.181818182x + x2 = 0 + 4.363636364 1.181818182x + x2 = 0 + 4.363636364 Combine like terms: 0 + 4.363636364 = 4.363636364 1.181818182x + x2 = 4.363636364 The x term is 1.181818182x. Take half its coefficient (0.590909091). Square it (0.3491735538) and add it to both sides. Add '0.3491735538' to each side of the equation. 1.181818182x + 0.3491735538 + x2 = 4.363636364 + 0.3491735538 Reorder the terms: 0.3491735538 + 1.181818182x + x2 = 4.363636364 + 0.3491735538 Combine like terms: 4.363636364 + 0.3491735538 = 4.7128099178 0.3491735538 + 1.181818182x + x2 = 4.7128099178 Factor a perfect square on the left side: (x + 0.590909091)(x + 0.590909091) = 4.7128099178 Calculate the square root of the right side: 2.170900716 Break this problem into two subproblems by setting (x + 0.590909091) equal to 2.170900716 and -2.170900716.Subproblem 1
x + 0.590909091 = 2.170900716 Simplifying x + 0.590909091 = 2.170900716 Reorder the terms: 0.590909091 + x = 2.170900716 Solving 0.590909091 + x = 2.170900716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.590909091' to each side of the equation. 0.590909091 + -0.590909091 + x = 2.170900716 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = 2.170900716 + -0.590909091 x = 2.170900716 + -0.590909091 Combine like terms: 2.170900716 + -0.590909091 = 1.579991625 x = 1.579991625 Simplifying x = 1.579991625Subproblem 2
x + 0.590909091 = -2.170900716 Simplifying x + 0.590909091 = -2.170900716 Reorder the terms: 0.590909091 + x = -2.170900716 Solving 0.590909091 + x = -2.170900716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.590909091' to each side of the equation. 0.590909091 + -0.590909091 + x = -2.170900716 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = -2.170900716 + -0.590909091 x = -2.170900716 + -0.590909091 Combine like terms: -2.170900716 + -0.590909091 = -2.761809807 x = -2.761809807 Simplifying x = -2.761809807Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.579991625, -2.761809807}
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