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Simplifying 4x2 + 31x + -30 = 0 Reorder the terms: -30 + 31x + 4x2 = 0 Solving -30 + 31x + 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'. -7.5 + 7.75x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 7.75x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 7.75x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 7.75x + x2 = 0 + 7.5 7.75x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 7.75x + x2 = 7.5 The x term is 7.75x. Take half its coefficient (3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. 7.75x + 15.015625 + x2 = 7.5 + 15.015625 Reorder the terms: 15.015625 + 7.75x + x2 = 7.5 + 15.015625 Combine like terms: 7.5 + 15.015625 = 22.515625 15.015625 + 7.75x + x2 = 22.515625 Factor a perfect square on the left side: (x + 3.875)(x + 3.875) = 22.515625 Calculate the square root of the right side: 4.745063224 Break this problem into two subproblems by setting (x + 3.875) equal to 4.745063224 and -4.745063224.Subproblem 1
x + 3.875 = 4.745063224 Simplifying x + 3.875 = 4.745063224 Reorder the terms: 3.875 + x = 4.745063224 Solving 3.875 + x = 4.745063224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + x = 4.745063224 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = 4.745063224 + -3.875 x = 4.745063224 + -3.875 Combine like terms: 4.745063224 + -3.875 = 0.870063224 x = 0.870063224 Simplifying x = 0.870063224Subproblem 2
x + 3.875 = -4.745063224 Simplifying x + 3.875 = -4.745063224 Reorder the terms: 3.875 + x = -4.745063224 Solving 3.875 + x = -4.745063224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + x = -4.745063224 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = -4.745063224 + -3.875 x = -4.745063224 + -3.875 Combine like terms: -4.745063224 + -3.875 = -8.620063224 x = -8.620063224 Simplifying x = -8.620063224Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.870063224, -8.620063224}
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