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Simplifying 49x2 + -86x + 30 = 0 Reorder the terms: 30 + -86x + 49x2 = 0 Solving 30 + -86x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.612244898 + -1.755102041x + x2 = 0 Move the constant term to the right: Add '-0.612244898' to each side of the equation. 0.612244898 + -1.755102041x + -0.612244898 + x2 = 0 + -0.612244898 Reorder the terms: 0.612244898 + -0.612244898 + -1.755102041x + x2 = 0 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + -1.755102041x + x2 = 0 + -0.612244898 -1.755102041x + x2 = 0 + -0.612244898 Combine like terms: 0 + -0.612244898 = -0.612244898 -1.755102041x + x2 = -0.612244898 The x term is -1.755102041x. Take half its coefficient (-0.8775510205). Square it (0.7700957936) and add it to both sides. Add '0.7700957936' to each side of the equation. -1.755102041x + 0.7700957936 + x2 = -0.612244898 + 0.7700957936 Reorder the terms: 0.7700957936 + -1.755102041x + x2 = -0.612244898 + 0.7700957936 Combine like terms: -0.612244898 + 0.7700957936 = 0.1578508956 0.7700957936 + -1.755102041x + x2 = 0.1578508956 Factor a perfect square on the left side: (x + -0.8775510205)(x + -0.8775510205) = 0.1578508956 Calculate the square root of the right side: 0.397304538 Break this problem into two subproblems by setting (x + -0.8775510205) equal to 0.397304538 and -0.397304538.Subproblem 1
x + -0.8775510205 = 0.397304538 Simplifying x + -0.8775510205 = 0.397304538 Reorder the terms: -0.8775510205 + x = 0.397304538 Solving -0.8775510205 + x = 0.397304538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8775510205' to each side of the equation. -0.8775510205 + 0.8775510205 + x = 0.397304538 + 0.8775510205 Combine like terms: -0.8775510205 + 0.8775510205 = 0.0000000000 0.0000000000 + x = 0.397304538 + 0.8775510205 x = 0.397304538 + 0.8775510205 Combine like terms: 0.397304538 + 0.8775510205 = 1.2748555585 x = 1.2748555585 Simplifying x = 1.2748555585Subproblem 2
x + -0.8775510205 = -0.397304538 Simplifying x + -0.8775510205 = -0.397304538 Reorder the terms: -0.8775510205 + x = -0.397304538 Solving -0.8775510205 + x = -0.397304538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8775510205' to each side of the equation. -0.8775510205 + 0.8775510205 + x = -0.397304538 + 0.8775510205 Combine like terms: -0.8775510205 + 0.8775510205 = 0.0000000000 0.0000000000 + x = -0.397304538 + 0.8775510205 x = -0.397304538 + 0.8775510205 Combine like terms: -0.397304538 + 0.8775510205 = 0.4802464825 x = 0.4802464825 Simplifying x = 0.4802464825Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2748555585, 0.4802464825}
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