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Simplifying 5x2 + 40x + 23 = 0 Reorder the terms: 23 + 40x + 5x2 = 0 Solving 23 + 40x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.6 + 8x + x2 = 0 Move the constant term to the right: Add '-4.6' to each side of the equation. 4.6 + 8x + -4.6 + x2 = 0 + -4.6 Reorder the terms: 4.6 + -4.6 + 8x + x2 = 0 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + 8x + x2 = 0 + -4.6 8x + x2 = 0 + -4.6 Combine like terms: 0 + -4.6 = -4.6 8x + x2 = -4.6 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -4.6 + 16 Reorder the terms: 16 + 8x + x2 = -4.6 + 16 Combine like terms: -4.6 + 16 = 11.4 16 + 8x + x2 = 11.4 Factor a perfect square on the left side: (x + 4)(x + 4) = 11.4 Calculate the square root of the right side: 3.376388603 Break this problem into two subproblems by setting (x + 4) equal to 3.376388603 and -3.376388603.Subproblem 1
x + 4 = 3.376388603 Simplifying x + 4 = 3.376388603 Reorder the terms: 4 + x = 3.376388603 Solving 4 + x = 3.376388603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.376388603 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.376388603 + -4 x = 3.376388603 + -4 Combine like terms: 3.376388603 + -4 = -0.623611397 x = -0.623611397 Simplifying x = -0.623611397Subproblem 2
x + 4 = -3.376388603 Simplifying x + 4 = -3.376388603 Reorder the terms: 4 + x = -3.376388603 Solving 4 + x = -3.376388603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.376388603 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.376388603 + -4 x = -3.376388603 + -4 Combine like terms: -3.376388603 + -4 = -7.376388603 x = -7.376388603 Simplifying x = -7.376388603Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.623611397, -7.376388603}
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