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Simplifying 4x2 + 7x + -136 = 0 Reorder the terms: -136 + 7x + 4x2 = 0 Solving -136 + 7x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -34 + 1.75x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + 1.75x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 1.75x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 1.75x + x2 = 0 + 34 1.75x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 1.75x + x2 = 34 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 34 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 34 + 0.765625 Combine like terms: 34 + 0.765625 = 34.765625 0.765625 + 1.75x + x2 = 34.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 34.765625 Calculate the square root of the right side: 5.896238208 Break this problem into two subproblems by setting (x + 0.875) equal to 5.896238208 and -5.896238208.Subproblem 1
x + 0.875 = 5.896238208 Simplifying x + 0.875 = 5.896238208 Reorder the terms: 0.875 + x = 5.896238208 Solving 0.875 + x = 5.896238208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 5.896238208 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 5.896238208 + -0.875 x = 5.896238208 + -0.875 Combine like terms: 5.896238208 + -0.875 = 5.021238208 x = 5.021238208 Simplifying x = 5.021238208Subproblem 2
x + 0.875 = -5.896238208 Simplifying x + 0.875 = -5.896238208 Reorder the terms: 0.875 + x = -5.896238208 Solving 0.875 + x = -5.896238208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -5.896238208 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -5.896238208 + -0.875 x = -5.896238208 + -0.875 Combine like terms: -5.896238208 + -0.875 = -6.771238208 x = -6.771238208 Simplifying x = -6.771238208Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.021238208, -6.771238208}
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