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Simplifying 18x2 + 5x = 3 + 7x Reorder the terms: 5x + 18x2 = 3 + 7x Solving 5x + 18x2 = 3 + 7x Solving for variable 'x'. Reorder the terms: -3 + 5x + -7x + 18x2 = 3 + 7x + -3 + -7x Combine like terms: 5x + -7x = -2x -3 + -2x + 18x2 = 3 + 7x + -3 + -7x Reorder the terms: -3 + -2x + 18x2 = 3 + -3 + 7x + -7x Combine like terms: 3 + -3 = 0 -3 + -2x + 18x2 = 0 + 7x + -7x -3 + -2x + 18x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -3 + -2x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.1666666667 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.1111111111x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.1111111111x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.1111111111x + x2 = 0 + 0.1666666667 -0.1111111111x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -0.1111111111x + x2 = 0.1666666667 The x term is -0.1111111111x. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111x + 0.003086419752 + x2 = 0.1666666667 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 0.1666666667 + 0.003086419752 Combine like terms: 0.1666666667 + 0.003086419752 = 0.169753086452 0.003086419752 + -0.1111111111x + x2 = 0.169753086452 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 0.169753086452 Calculate the square root of the right side: 0.412011027 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 0.412011027 and -0.412011027.Subproblem 1
x + -0.05555555555 = 0.412011027 Simplifying x + -0.05555555555 = 0.412011027 Reorder the terms: -0.05555555555 + x = 0.412011027 Solving -0.05555555555 + x = 0.412011027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 0.412011027 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 0.412011027 + 0.05555555555 x = 0.412011027 + 0.05555555555 Combine like terms: 0.412011027 + 0.05555555555 = 0.46756658255 x = 0.46756658255 Simplifying x = 0.46756658255Subproblem 2
x + -0.05555555555 = -0.412011027 Simplifying x + -0.05555555555 = -0.412011027 Reorder the terms: -0.05555555555 + x = -0.412011027 Solving -0.05555555555 + x = -0.412011027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -0.412011027 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -0.412011027 + 0.05555555555 x = -0.412011027 + 0.05555555555 Combine like terms: -0.412011027 + 0.05555555555 = -0.35645547145 x = -0.35645547145 Simplifying x = -0.35645547145Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.46756658255, -0.35645547145}
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