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Simplifying 50 = 3x2 + 4.7x + 10.3 Reorder the terms: 50 = 10.3 + 4.7x + 3x2 Solving 50 = 10.3 + 4.7x + 3x2 Solving for variable 'x'. Combine like terms: 50 + -10.3 = 39.7 39.7 + -4.7x + -3x2 = 10.3 + 4.7x + 3x2 + -10.3 + -4.7x + -3x2 Reorder the terms: 39.7 + -4.7x + -3x2 = 10.3 + -10.3 + 4.7x + -4.7x + 3x2 + -3x2 Combine like terms: 10.3 + -10.3 = 0.0 39.7 + -4.7x + -3x2 = 0.0 + 4.7x + -4.7x + 3x2 + -3x2 39.7 + -4.7x + -3x2 = 4.7x + -4.7x + 3x2 + -3x2 Combine like terms: 4.7x + -4.7x = 0.0 39.7 + -4.7x + -3x2 = 0.0 + 3x2 + -3x2 39.7 + -4.7x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 39.7 + -4.7x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -13.23333333 + 1.566666667x + x2 = 0 Move the constant term to the right: Add '13.23333333' to each side of the equation. -13.23333333 + 1.566666667x + 13.23333333 + x2 = 0 + 13.23333333 Reorder the terms: -13.23333333 + 13.23333333 + 1.566666667x + x2 = 0 + 13.23333333 Combine like terms: -13.23333333 + 13.23333333 = 0.00000000 0.00000000 + 1.566666667x + x2 = 0 + 13.23333333 1.566666667x + x2 = 0 + 13.23333333 Combine like terms: 0 + 13.23333333 = 13.23333333 1.566666667x + x2 = 13.23333333 The x term is 1.566666667x. Take half its coefficient (0.7833333335). Square it (0.6136111114) and add it to both sides. Add '0.6136111114' to each side of the equation. 1.566666667x + 0.6136111114 + x2 = 13.23333333 + 0.6136111114 Reorder the terms: 0.6136111114 + 1.566666667x + x2 = 13.23333333 + 0.6136111114 Combine like terms: 13.23333333 + 0.6136111114 = 13.8469444414 0.6136111114 + 1.566666667x + x2 = 13.8469444414 Factor a perfect square on the left side: (x + 0.7833333335)(x + 0.7833333335) = 13.8469444414 Calculate the square root of the right side: 3.721148269 Break this problem into two subproblems by setting (x + 0.7833333335) equal to 3.721148269 and -3.721148269.Subproblem 1
x + 0.7833333335 = 3.721148269 Simplifying x + 0.7833333335 = 3.721148269 Reorder the terms: 0.7833333335 + x = 3.721148269 Solving 0.7833333335 + x = 3.721148269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7833333335' to each side of the equation. 0.7833333335 + -0.7833333335 + x = 3.721148269 + -0.7833333335 Combine like terms: 0.7833333335 + -0.7833333335 = 0.0000000000 0.0000000000 + x = 3.721148269 + -0.7833333335 x = 3.721148269 + -0.7833333335 Combine like terms: 3.721148269 + -0.7833333335 = 2.9378149355 x = 2.9378149355 Simplifying x = 2.9378149355Subproblem 2
x + 0.7833333335 = -3.721148269 Simplifying x + 0.7833333335 = -3.721148269 Reorder the terms: 0.7833333335 + x = -3.721148269 Solving 0.7833333335 + x = -3.721148269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7833333335' to each side of the equation. 0.7833333335 + -0.7833333335 + x = -3.721148269 + -0.7833333335 Combine like terms: 0.7833333335 + -0.7833333335 = 0.0000000000 0.0000000000 + x = -3.721148269 + -0.7833333335 x = -3.721148269 + -0.7833333335 Combine like terms: -3.721148269 + -0.7833333335 = -4.5044816025 x = -4.5044816025 Simplifying x = -4.5044816025Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9378149355, -4.5044816025}
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