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Simplifying 49.3x2 + -74.62x + 26.117 = 0 Reorder the terms: 26.117 + -74.62x + 49.3x2 = 0 Solving 26.117 + -74.62x + 49.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49.3 the coefficient of the squared term: Divide each side by '49.3'. 0.5297565923 + -1.513590264x + x2 = 0 Move the constant term to the right: Add '-0.5297565923' to each side of the equation. 0.5297565923 + -1.513590264x + -0.5297565923 + x2 = 0 + -0.5297565923 Reorder the terms: 0.5297565923 + -0.5297565923 + -1.513590264x + x2 = 0 + -0.5297565923 Combine like terms: 0.5297565923 + -0.5297565923 = 0.0000000000 0.0000000000 + -1.513590264x + x2 = 0 + -0.5297565923 -1.513590264x + x2 = 0 + -0.5297565923 Combine like terms: 0 + -0.5297565923 = -0.5297565923 -1.513590264x + x2 = -0.5297565923 The x term is -1.513590264x. Take half its coefficient (-0.756795132). Square it (0.5727388718) and add it to both sides. Add '0.5727388718' to each side of the equation. -1.513590264x + 0.5727388718 + x2 = -0.5297565923 + 0.5727388718 Reorder the terms: 0.5727388718 + -1.513590264x + x2 = -0.5297565923 + 0.5727388718 Combine like terms: -0.5297565923 + 0.5727388718 = 0.0429822795 0.5727388718 + -1.513590264x + x2 = 0.0429822795 Factor a perfect square on the left side: (x + -0.756795132)(x + -0.756795132) = 0.0429822795 Calculate the square root of the right side: 0.207321681 Break this problem into two subproblems by setting (x + -0.756795132) equal to 0.207321681 and -0.207321681.Subproblem 1
x + -0.756795132 = 0.207321681 Simplifying x + -0.756795132 = 0.207321681 Reorder the terms: -0.756795132 + x = 0.207321681 Solving -0.756795132 + x = 0.207321681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.756795132' to each side of the equation. -0.756795132 + 0.756795132 + x = 0.207321681 + 0.756795132 Combine like terms: -0.756795132 + 0.756795132 = 0.000000000 0.000000000 + x = 0.207321681 + 0.756795132 x = 0.207321681 + 0.756795132 Combine like terms: 0.207321681 + 0.756795132 = 0.964116813 x = 0.964116813 Simplifying x = 0.964116813Subproblem 2
x + -0.756795132 = -0.207321681 Simplifying x + -0.756795132 = -0.207321681 Reorder the terms: -0.756795132 + x = -0.207321681 Solving -0.756795132 + x = -0.207321681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.756795132' to each side of the equation. -0.756795132 + 0.756795132 + x = -0.207321681 + 0.756795132 Combine like terms: -0.756795132 + 0.756795132 = 0.000000000 0.000000000 + x = -0.207321681 + 0.756795132 x = -0.207321681 + 0.756795132 Combine like terms: -0.207321681 + 0.756795132 = 0.549473451 x = 0.549473451 Simplifying x = 0.549473451Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.964116813, 0.549473451}
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