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Simplifying 23x2 + 34x = 1 Reorder the terms: 34x + 23x2 = 1 Solving 34x + 23x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 34x + 23x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 34x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.04347826087 + 1.47826087x + x2 = 0 Move the constant term to the right: Add '0.04347826087' to each side of the equation. -0.04347826087 + 1.47826087x + 0.04347826087 + x2 = 0 + 0.04347826087 Reorder the terms: -0.04347826087 + 0.04347826087 + 1.47826087x + x2 = 0 + 0.04347826087 Combine like terms: -0.04347826087 + 0.04347826087 = 0.00000000000 0.00000000000 + 1.47826087x + x2 = 0 + 0.04347826087 1.47826087x + x2 = 0 + 0.04347826087 Combine like terms: 0 + 0.04347826087 = 0.04347826087 1.47826087x + x2 = 0.04347826087 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 = 0.04347826087 + 0.5463137999 Reorder the terms: 0.5463137999 + 1.47826087x + x2 = 0.04347826087 + 0.5463137999 Combine like terms: 0.04347826087 + 0.5463137999 = 0.58979206077 0.5463137999 + 1.47826087x + x2 = 0.58979206077 Factor a perfect square on the left side: (x + 0.739130435)(x + 0.739130435) = 0.58979206077 Calculate the square root of the right side: 0.767979206 Break this problem into two subproblems by setting (x + 0.739130435) equal to 0.767979206 and -0.767979206.Subproblem 1
x + 0.739130435 = 0.767979206 Simplifying x + 0.739130435 = 0.767979206 Reorder the terms: 0.739130435 + x = 0.767979206 Solving 0.739130435 + x = 0.767979206 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 = 0.767979206 + -0.739130435 Combine like terms: 0.739130435 + -0.739130435 = 0.000000000 0.000000000 + x = 0.767979206 + -0.739130435 x = 0.767979206 + -0.739130435 Combine like terms: 0.767979206 + -0.739130435 = 0.028848771 x = 0.028848771 Simplifying x = 0.028848771Subproblem 2
x + 0.739130435 = -0.767979206 Simplifying x + 0.739130435 = -0.767979206 Reorder the terms: 0.739130435 + x = -0.767979206 Solving 0.739130435 + x = -0.767979206 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 = -0.767979206 + -0.739130435 Combine like terms: 0.739130435 + -0.739130435 = 0.000000000 0.000000000 + x = -0.767979206 + -0.739130435 x = -0.767979206 + -0.739130435 Combine like terms: -0.767979206 + -0.739130435 = -1.507109641 x = -1.507109641 Simplifying x = -1.507109641Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.028848771, -1.507109641}
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