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Simplifying 7x + 23x2 = 99 Solving 7x + 23x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + 7x + 23x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 7x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -4.304347826 + 0.3043478261x + x2 = 0 Move the constant term to the right: Add '4.304347826' to each side of the equation. -4.304347826 + 0.3043478261x + 4.304347826 + x2 = 0 + 4.304347826 Reorder the terms: -4.304347826 + 4.304347826 + 0.3043478261x + x2 = 0 + 4.304347826 Combine like terms: -4.304347826 + 4.304347826 = 0.000000000 0.000000000 + 0.3043478261x + x2 = 0 + 4.304347826 0.3043478261x + x2 = 0 + 4.304347826 Combine like terms: 0 + 4.304347826 = 4.304347826 0.3043478261x + x2 = 4.304347826 The x term is 0.3043478261x. Take half its coefficient (0.1521739131). Square it (0.02315689983) and add it to both sides. Add '0.02315689983' to each side of the equation. 0.3043478261x + 0.02315689983 + x2 = 4.304347826 + 0.02315689983 Reorder the terms: 0.02315689983 + 0.3043478261x + x2 = 4.304347826 + 0.02315689983 Combine like terms: 4.304347826 + 0.02315689983 = 4.32750472583 0.02315689983 + 0.3043478261x + x2 = 4.32750472583 Factor a perfect square on the left side: (x + 0.1521739131)(x + 0.1521739131) = 4.32750472583 Calculate the square root of the right side: 2.080265542 Break this problem into two subproblems by setting (x + 0.1521739131) equal to 2.080265542 and -2.080265542.Subproblem 1
x + 0.1521739131 = 2.080265542 Simplifying x + 0.1521739131 = 2.080265542 Reorder the terms: 0.1521739131 + x = 2.080265542 Solving 0.1521739131 + x = 2.080265542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1521739131' to each side of the equation. 0.1521739131 + -0.1521739131 + x = 2.080265542 + -0.1521739131 Combine like terms: 0.1521739131 + -0.1521739131 = 0.0000000000 0.0000000000 + x = 2.080265542 + -0.1521739131 x = 2.080265542 + -0.1521739131 Combine like terms: 2.080265542 + -0.1521739131 = 1.9280916289 x = 1.9280916289 Simplifying x = 1.9280916289Subproblem 2
x + 0.1521739131 = -2.080265542 Simplifying x + 0.1521739131 = -2.080265542 Reorder the terms: 0.1521739131 + x = -2.080265542 Solving 0.1521739131 + x = -2.080265542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1521739131' to each side of the equation. 0.1521739131 + -0.1521739131 + x = -2.080265542 + -0.1521739131 Combine like terms: 0.1521739131 + -0.1521739131 = 0.0000000000 0.0000000000 + x = -2.080265542 + -0.1521739131 x = -2.080265542 + -0.1521739131 Combine like terms: -2.080265542 + -0.1521739131 = -2.2324394551 x = -2.2324394551 Simplifying x = -2.2324394551Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9280916289, -2.2324394551}
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