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Simplifying 5x2 + 40x + 5 = 4x Reorder the terms: 5 + 40x + 5x2 = 4x Solving 5 + 40x + 5x2 = 4x Solving for variable 'x'. Reorder the terms: 5 + 40x + -4x + 5x2 = 4x + -4x Combine like terms: 40x + -4x = 36x 5 + 36x + 5x2 = 4x + -4x Combine like terms: 4x + -4x = 0 5 + 36x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 7.2x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 7.2x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 7.2x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7.2x + x2 = 0 + -1 7.2x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 7.2x + x2 = -1 The x term is 7.2x. Take half its coefficient (3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. 7.2x + 12.96 + x2 = -1 + 12.96 Reorder the terms: 12.96 + 7.2x + x2 = -1 + 12.96 Combine like terms: -1 + 12.96 = 11.96 12.96 + 7.2x + x2 = 11.96 Factor a perfect square on the left side: (x + 3.6)(x + 3.6) = 11.96 Calculate the square root of the right side: 3.458323293 Break this problem into two subproblems by setting (x + 3.6) equal to 3.458323293 and -3.458323293.Subproblem 1
x + 3.6 = 3.458323293 Simplifying x + 3.6 = 3.458323293 Reorder the terms: 3.6 + x = 3.458323293 Solving 3.6 + x = 3.458323293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = 3.458323293 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = 3.458323293 + -3.6 x = 3.458323293 + -3.6 Combine like terms: 3.458323293 + -3.6 = -0.141676707 x = -0.141676707 Simplifying x = -0.141676707Subproblem 2
x + 3.6 = -3.458323293 Simplifying x + 3.6 = -3.458323293 Reorder the terms: 3.6 + x = -3.458323293 Solving 3.6 + x = -3.458323293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = -3.458323293 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = -3.458323293 + -3.6 x = -3.458323293 + -3.6 Combine like terms: -3.458323293 + -3.6 = -7.058323293 x = -7.058323293 Simplifying x = -7.058323293Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.141676707, -7.058323293}
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