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Simplifying 23x2 + -34x + -3 = 0 Reorder the terms: -3 + -34x + 23x2 = 0 Solving -3 + -34x + 23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.1304347826 + -1.47826087x + x2 = 0 Move the constant term to the right: Add '0.1304347826' to each side of the equation. -0.1304347826 + -1.47826087x + 0.1304347826 + x2 = 0 + 0.1304347826 Reorder the terms: -0.1304347826 + 0.1304347826 + -1.47826087x + x2 = 0 + 0.1304347826 Combine like terms: -0.1304347826 + 0.1304347826 = 0.0000000000 0.0000000000 + -1.47826087x + x2 = 0 + 0.1304347826 -1.47826087x + x2 = 0 + 0.1304347826 Combine like terms: 0 + 0.1304347826 = 0.1304347826 -1.47826087x + x2 = 0.1304347826 The x term is -1.47826087x. Take half its coefficient (-0.739130435). Square it (0.5463137999) and add it to both sides. Add '0.5463137999' to each side of the equation. -1.47826087x + 0.5463137999 + x2 = 0.1304347826 + 0.5463137999 Reorder the terms: 0.5463137999 + -1.47826087x + x2 = 0.1304347826 + 0.5463137999 Combine like terms: 0.1304347826 + 0.5463137999 = 0.6767485825 0.5463137999 + -1.47826087x + x2 = 0.6767485825 Factor a perfect square on the left side: (x + -0.739130435)(x + -0.739130435) = 0.6767485825 Calculate the square root of the right side: 0.822647301 Break this problem into two subproblems by setting (x + -0.739130435) equal to 0.822647301 and -0.822647301.Subproblem 1
x + -0.739130435 = 0.822647301 Simplifying x + -0.739130435 = 0.822647301 Reorder the terms: -0.739130435 + x = 0.822647301 Solving -0.739130435 + x = 0.822647301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.739130435' to each side of the equation. -0.739130435 + 0.739130435 + x = 0.822647301 + 0.739130435 Combine like terms: -0.739130435 + 0.739130435 = 0.000000000 0.000000000 + x = 0.822647301 + 0.739130435 x = 0.822647301 + 0.739130435 Combine like terms: 0.822647301 + 0.739130435 = 1.561777736 x = 1.561777736 Simplifying x = 1.561777736Subproblem 2
x + -0.739130435 = -0.822647301 Simplifying x + -0.739130435 = -0.822647301 Reorder the terms: -0.739130435 + x = -0.822647301 Solving -0.739130435 + x = -0.822647301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.739130435' to each side of the equation. -0.739130435 + 0.739130435 + x = -0.822647301 + 0.739130435 Combine like terms: -0.739130435 + 0.739130435 = 0.000000000 0.000000000 + x = -0.822647301 + 0.739130435 x = -0.822647301 + 0.739130435 Combine like terms: -0.822647301 + 0.739130435 = -0.083516866 x = -0.083516866 Simplifying x = -0.083516866Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.561777736, -0.083516866}
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