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Simplifying 13x2 + 50x + -400 = 0 Reorder the terms: -400 + 50x + 13x2 = 0 Solving -400 + 50x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -30.76923077 + 3.846153846x + x2 = 0 Move the constant term to the right: Add '30.76923077' to each side of the equation. -30.76923077 + 3.846153846x + 30.76923077 + x2 = 0 + 30.76923077 Reorder the terms: -30.76923077 + 30.76923077 + 3.846153846x + x2 = 0 + 30.76923077 Combine like terms: -30.76923077 + 30.76923077 = 0.00000000 0.00000000 + 3.846153846x + x2 = 0 + 30.76923077 3.846153846x + x2 = 0 + 30.76923077 Combine like terms: 0 + 30.76923077 = 30.76923077 3.846153846x + x2 = 30.76923077 The x term is 3.846153846x. Take half its coefficient (1.923076923). Square it (3.698224852) and add it to both sides. Add '3.698224852' to each side of the equation. 3.846153846x + 3.698224852 + x2 = 30.76923077 + 3.698224852 Reorder the terms: 3.698224852 + 3.846153846x + x2 = 30.76923077 + 3.698224852 Combine like terms: 30.76923077 + 3.698224852 = 34.467455622 3.698224852 + 3.846153846x + x2 = 34.467455622 Factor a perfect square on the left side: (x + 1.923076923)(x + 1.923076923) = 34.467455622 Calculate the square root of the right side: 5.870899047 Break this problem into two subproblems by setting (x + 1.923076923) equal to 5.870899047 and -5.870899047.Subproblem 1
x + 1.923076923 = 5.870899047 Simplifying x + 1.923076923 = 5.870899047 Reorder the terms: 1.923076923 + x = 5.870899047 Solving 1.923076923 + x = 5.870899047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.923076923' to each side of the equation. 1.923076923 + -1.923076923 + x = 5.870899047 + -1.923076923 Combine like terms: 1.923076923 + -1.923076923 = 0.000000000 0.000000000 + x = 5.870899047 + -1.923076923 x = 5.870899047 + -1.923076923 Combine like terms: 5.870899047 + -1.923076923 = 3.947822124 x = 3.947822124 Simplifying x = 3.947822124Subproblem 2
x + 1.923076923 = -5.870899047 Simplifying x + 1.923076923 = -5.870899047 Reorder the terms: 1.923076923 + x = -5.870899047 Solving 1.923076923 + x = -5.870899047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.923076923' to each side of the equation. 1.923076923 + -1.923076923 + x = -5.870899047 + -1.923076923 Combine like terms: 1.923076923 + -1.923076923 = 0.000000000 0.000000000 + x = -5.870899047 + -1.923076923 x = -5.870899047 + -1.923076923 Combine like terms: -5.870899047 + -1.923076923 = -7.79397597 x = -7.79397597 Simplifying x = -7.79397597Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.947822124, -7.79397597}
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