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Simplifying 2x2 + 7x + -152 = 0 Reorder the terms: -152 + 7x + 2x2 = 0 Solving -152 + 7x + 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'. -76 + 3.5x + x2 = 0 Move the constant term to the right: Add '76' to each side of the equation. -76 + 3.5x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 3.5x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 3.5x + x2 = 0 + 76 3.5x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 3.5x + x2 = 76 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 76 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 76 + 3.0625 Combine like terms: 76 + 3.0625 = 79.0625 3.0625 + 3.5x + x2 = 79.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 79.0625 Calculate the square root of the right side: 8.891709622 Break this problem into two subproblems by setting (x + 1.75) equal to 8.891709622 and -8.891709622.Subproblem 1
x + 1.75 = 8.891709622 Simplifying x + 1.75 = 8.891709622 Reorder the terms: 1.75 + x = 8.891709622 Solving 1.75 + x = 8.891709622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 8.891709622 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 8.891709622 + -1.75 x = 8.891709622 + -1.75 Combine like terms: 8.891709622 + -1.75 = 7.141709622 x = 7.141709622 Simplifying x = 7.141709622Subproblem 2
x + 1.75 = -8.891709622 Simplifying x + 1.75 = -8.891709622 Reorder the terms: 1.75 + x = -8.891709622 Solving 1.75 + x = -8.891709622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -8.891709622 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -8.891709622 + -1.75 x = -8.891709622 + -1.75 Combine like terms: -8.891709622 + -1.75 = -10.641709622 x = -10.641709622 Simplifying x = -10.641709622Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.141709622, -10.641709622}
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