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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 = 0.4158790173 0.5463137999 + 1.47826087x + x2 = 0.4158790173 Factor a perfect square on the left side: (x + 0.739130435)(x + 0.739130435) = 0.4158790173 Calculate the square root of the right side: 0.644886825 Break this problem into two subproblems by setting (x + 0.739130435) equal to 0.644886825 and -0.644886825.Subproblem 1
x + 0.739130435 = 0.644886825 Simplifying x + 0.739130435 = 0.644886825 Reorder the terms: 0.739130435 + x = 0.644886825 Solving 0.739130435 + x = 0.644886825 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 = 0.644886825 + -0.739130435 Combine like terms: 0.739130435 + -0.739130435 = 0.000000000 0.000000000 + x = 0.644886825 + -0.739130435 x = 0.644886825 + -0.739130435 Combine like terms: 0.644886825 + -0.739130435 = -0.09424361 x = -0.09424361 Simplifying x = -0.09424361Subproblem 2
x + 0.739130435 = -0.644886825 Simplifying x + 0.739130435 = -0.644886825 Reorder the terms: 0.739130435 + x = -0.644886825 Solving 0.739130435 + x = -0.644886825 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 = -0.644886825 + -0.739130435 Combine like terms: 0.739130435 + -0.739130435 = 0.000000000 0.000000000 + x = -0.644886825 + -0.739130435 x = -0.644886825 + -0.739130435 Combine like terms: -0.644886825 + -0.739130435 = -1.38401726 x = -1.38401726 Simplifying x = -1.38401726Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.09424361, -1.38401726}
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