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Simplifying 2x2 + 28x + -507 = 0 Reorder the terms: -507 + 28x + 2x2 = 0 Solving -507 + 28x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -253.5 + 14x + x2 = 0 Move the constant term to the right: Add '253.5' to each side of the equation. -253.5 + 14x + 253.5 + x2 = 0 + 253.5 Reorder the terms: -253.5 + 253.5 + 14x + x2 = 0 + 253.5 Combine like terms: -253.5 + 253.5 = 0.0 0.0 + 14x + x2 = 0 + 253.5 14x + x2 = 0 + 253.5 Combine like terms: 0 + 253.5 = 253.5 14x + x2 = 253.5 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 253.5 + 49 Reorder the terms: 49 + 14x + x2 = 253.5 + 49 Combine like terms: 253.5 + 49 = 302.5 49 + 14x + x2 = 302.5 Factor a perfect square on the left side: (x + 7)(x + 7) = 302.5 Calculate the square root of the right side: 17.392527131 Break this problem into two subproblems by setting (x + 7) equal to 17.392527131 and -17.392527131.Subproblem 1
x + 7 = 17.392527131 Simplifying x + 7 = 17.392527131 Reorder the terms: 7 + x = 17.392527131 Solving 7 + x = 17.392527131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 17.392527131 + -7 Combine like terms: 7 + -7 = 0 0 + x = 17.392527131 + -7 x = 17.392527131 + -7 Combine like terms: 17.392527131 + -7 = 10.392527131 x = 10.392527131 Simplifying x = 10.392527131Subproblem 2
x + 7 = -17.392527131 Simplifying x + 7 = -17.392527131 Reorder the terms: 7 + x = -17.392527131 Solving 7 + x = -17.392527131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -17.392527131 + -7 Combine like terms: 7 + -7 = 0 0 + x = -17.392527131 + -7 x = -17.392527131 + -7 Combine like terms: -17.392527131 + -7 = -24.392527131 x = -24.392527131 Simplifying x = -24.392527131Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.392527131, -24.392527131}
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