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Simplifying x + -4 + 23x2 = 0 Reorder the terms: -4 + x + 23x2 = 0 Solving -4 + x + 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'. -0.1739130435 + 0.04347826087x + x2 = 0 Move the constant term to the right: Add '0.1739130435' to each side of the equation. -0.1739130435 + 0.04347826087x + 0.1739130435 + x2 = 0 + 0.1739130435 Reorder the terms: -0.1739130435 + 0.1739130435 + 0.04347826087x + x2 = 0 + 0.1739130435 Combine like terms: -0.1739130435 + 0.1739130435 = 0.0000000000 0.0000000000 + 0.04347826087x + x2 = 0 + 0.1739130435 0.04347826087x + x2 = 0 + 0.1739130435 Combine like terms: 0 + 0.1739130435 = 0.1739130435 0.04347826087x + x2 = 0.1739130435 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.04347826087x + 0.25 + x2 = 0.1739130435 + 0.25 Reorder the terms: 0.25 + 0.04347826087x + x2 = 0.1739130435 + 0.25 Combine like terms: 0.1739130435 + 0.25 = 0.4239130435 0.25 + 0.04347826087x + x2 = 0.4239130435 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4239130435 Calculate the square root of the right side: 0.651086049 Break this problem into two subproblems by setting (x + 0.5) equal to 0.651086049 and -0.651086049.Subproblem 1
x + 0.5 = 0.651086049 Simplifying x + 0.5 = 0.651086049 Reorder the terms: 0.5 + x = 0.651086049 Solving 0.5 + x = 0.651086049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.651086049 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.651086049 + -0.5 x = 0.651086049 + -0.5 Combine like terms: 0.651086049 + -0.5 = 0.151086049 x = 0.151086049 Simplifying x = 0.151086049Subproblem 2
x + 0.5 = -0.651086049 Simplifying x + 0.5 = -0.651086049 Reorder the terms: 0.5 + x = -0.651086049 Solving 0.5 + x = -0.651086049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.651086049 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.651086049 + -0.5 x = -0.651086049 + -0.5 Combine like terms: -0.651086049 + -0.5 = -1.151086049 x = -1.151086049 Simplifying x = -1.151086049Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.151086049, -1.151086049}
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