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Simplifying 2.3x2 + -4x + -7.1 = 0 Reorder the terms: -7.1 + -4x + 2.3x2 = 0 Solving -7.1 + -4x + 2.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.3 the coefficient of the squared term: Divide each side by '2.3'. -3.086956522 + -1.739130435x + x2 = 0 Move the constant term to the right: Add '3.086956522' to each side of the equation. -3.086956522 + -1.739130435x + 3.086956522 + x2 = 0 + 3.086956522 Reorder the terms: -3.086956522 + 3.086956522 + -1.739130435x + x2 = 0 + 3.086956522 Combine like terms: -3.086956522 + 3.086956522 = 0.000000000 0.000000000 + -1.739130435x + x2 = 0 + 3.086956522 -1.739130435x + x2 = 0 + 3.086956522 Combine like terms: 0 + 3.086956522 = 3.086956522 -1.739130435x + x2 = 3.086956522 The x term is -1.739130435x. Take half its coefficient (-0.8695652175). Square it (0.7561436675) and add it to both sides. Add '0.7561436675' to each side of the equation. -1.739130435x + 0.7561436675 + x2 = 3.086956522 + 0.7561436675 Reorder the terms: 0.7561436675 + -1.739130435x + x2 = 3.086956522 + 0.7561436675 Combine like terms: 3.086956522 + 0.7561436675 = 3.8431001895 0.7561436675 + -1.739130435x + x2 = 3.8431001895 Factor a perfect square on the left side: (x + -0.8695652175)(x + -0.8695652175) = 3.8431001895 Calculate the square root of the right side: 1.960382664 Break this problem into two subproblems by setting (x + -0.8695652175) equal to 1.960382664 and -1.960382664.Subproblem 1
x + -0.8695652175 = 1.960382664 Simplifying x + -0.8695652175 = 1.960382664 Reorder the terms: -0.8695652175 + x = 1.960382664 Solving -0.8695652175 + x = 1.960382664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8695652175' to each side of the equation. -0.8695652175 + 0.8695652175 + x = 1.960382664 + 0.8695652175 Combine like terms: -0.8695652175 + 0.8695652175 = 0.0000000000 0.0000000000 + x = 1.960382664 + 0.8695652175 x = 1.960382664 + 0.8695652175 Combine like terms: 1.960382664 + 0.8695652175 = 2.8299478815 x = 2.8299478815 Simplifying x = 2.8299478815Subproblem 2
x + -0.8695652175 = -1.960382664 Simplifying x + -0.8695652175 = -1.960382664 Reorder the terms: -0.8695652175 + x = -1.960382664 Solving -0.8695652175 + x = -1.960382664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8695652175' to each side of the equation. -0.8695652175 + 0.8695652175 + x = -1.960382664 + 0.8695652175 Combine like terms: -0.8695652175 + 0.8695652175 = 0.0000000000 0.0000000000 + x = -1.960382664 + 0.8695652175 x = -1.960382664 + 0.8695652175 Combine like terms: -1.960382664 + 0.8695652175 = -1.0908174465 x = -1.0908174465 Simplifying x = -1.0908174465Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8299478815, -1.0908174465}
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