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Simplifying 23x2 + 8x = 6 Reorder the terms: 8x + 23x2 = 6 Solving 8x + 23x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 8x + 23x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 8x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.2608695652 + 0.347826087x + x2 = 0 Move the constant term to the right: Add '0.2608695652' to each side of the equation. -0.2608695652 + 0.347826087x + 0.2608695652 + x2 = 0 + 0.2608695652 Reorder the terms: -0.2608695652 + 0.2608695652 + 0.347826087x + x2 = 0 + 0.2608695652 Combine like terms: -0.2608695652 + 0.2608695652 = 0.0000000000 0.0000000000 + 0.347826087x + x2 = 0 + 0.2608695652 0.347826087x + x2 = 0 + 0.2608695652 Combine like terms: 0 + 0.2608695652 = 0.2608695652 0.347826087x + x2 = 0.2608695652 The x term is 0.347826087x. Take half its coefficient (0.1739130435). Square it (0.03024574670) and add it to both sides. Add '0.03024574670' to each side of the equation. 0.347826087x + 0.03024574670 + x2 = 0.2608695652 + 0.03024574670 Reorder the terms: 0.03024574670 + 0.347826087x + x2 = 0.2608695652 + 0.03024574670 Combine like terms: 0.2608695652 + 0.03024574670 = 0.2911153119 0.03024574670 + 0.347826087x + x2 = 0.2911153119 Factor a perfect square on the left side: (x + 0.1739130435)(x + 0.1739130435) = 0.2911153119 Calculate the square root of the right side: 0.539551028 Break this problem into two subproblems by setting (x + 0.1739130435) equal to 0.539551028 and -0.539551028.Subproblem 1
x + 0.1739130435 = 0.539551028 Simplifying x + 0.1739130435 = 0.539551028 Reorder the terms: 0.1739130435 + x = 0.539551028 Solving 0.1739130435 + x = 0.539551028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1739130435' to each side of the equation. 0.1739130435 + -0.1739130435 + x = 0.539551028 + -0.1739130435 Combine like terms: 0.1739130435 + -0.1739130435 = 0.0000000000 0.0000000000 + x = 0.539551028 + -0.1739130435 x = 0.539551028 + -0.1739130435 Combine like terms: 0.539551028 + -0.1739130435 = 0.3656379845 x = 0.3656379845 Simplifying x = 0.3656379845Subproblem 2
x + 0.1739130435 = -0.539551028 Simplifying x + 0.1739130435 = -0.539551028 Reorder the terms: 0.1739130435 + x = -0.539551028 Solving 0.1739130435 + x = -0.539551028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1739130435' to each side of the equation. 0.1739130435 + -0.1739130435 + x = -0.539551028 + -0.1739130435 Combine like terms: 0.1739130435 + -0.1739130435 = 0.0000000000 0.0000000000 + x = -0.539551028 + -0.1739130435 x = -0.539551028 + -0.1739130435 Combine like terms: -0.539551028 + -0.1739130435 = -0.7134640715 x = -0.7134640715 Simplifying x = -0.7134640715Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3656379845, -0.7134640715}
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