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Simplifying 5x2 + 26x + -236 = 0 Reorder the terms: -236 + 26x + 5x2 = 0 Solving -236 + 26x + 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'. -47.2 + 5.2x + x2 = 0 Move the constant term to the right: Add '47.2' to each side of the equation. -47.2 + 5.2x + 47.2 + x2 = 0 + 47.2 Reorder the terms: -47.2 + 47.2 + 5.2x + x2 = 0 + 47.2 Combine like terms: -47.2 + 47.2 = 0.0 0.0 + 5.2x + x2 = 0 + 47.2 5.2x + x2 = 0 + 47.2 Combine like terms: 0 + 47.2 = 47.2 5.2x + x2 = 47.2 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = 47.2 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 47.2 + 6.76 Combine like terms: 47.2 + 6.76 = 53.96 6.76 + 5.2x + x2 = 53.96 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 53.96 Calculate the square root of the right side: 7.345747069 Break this problem into two subproblems by setting (x + 2.6) equal to 7.345747069 and -7.345747069.Subproblem 1
x + 2.6 = 7.345747069 Simplifying x + 2.6 = 7.345747069 Reorder the terms: 2.6 + x = 7.345747069 Solving 2.6 + x = 7.345747069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 7.345747069 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 7.345747069 + -2.6 x = 7.345747069 + -2.6 Combine like terms: 7.345747069 + -2.6 = 4.745747069 x = 4.745747069 Simplifying x = 4.745747069Subproblem 2
x + 2.6 = -7.345747069 Simplifying x + 2.6 = -7.345747069 Reorder the terms: 2.6 + x = -7.345747069 Solving 2.6 + x = -7.345747069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -7.345747069 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -7.345747069 + -2.6 x = -7.345747069 + -2.6 Combine like terms: -7.345747069 + -2.6 = -9.945747069 x = -9.945747069 Simplifying x = -9.945747069Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.745747069, -9.945747069}
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