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Simplifying 4x2 + -15x + -76 = 0 Reorder the terms: -76 + -15x + 4x2 = 0 Solving -76 + -15x + 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'. -19 + -3.75x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -3.75x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -3.75x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -3.75x + x2 = 0 + 19 -3.75x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -3.75x + x2 = 19 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 19 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 19 + 3.515625 Combine like terms: 19 + 3.515625 = 22.515625 3.515625 + -3.75x + x2 = 22.515625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 22.515625 Calculate the square root of the right side: 4.745063224 Break this problem into two subproblems by setting (x + -1.875) equal to 4.745063224 and -4.745063224.Subproblem 1
x + -1.875 = 4.745063224 Simplifying x + -1.875 = 4.745063224 Reorder the terms: -1.875 + x = 4.745063224 Solving -1.875 + x = 4.745063224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 4.745063224 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 4.745063224 + 1.875 x = 4.745063224 + 1.875 Combine like terms: 4.745063224 + 1.875 = 6.620063224 x = 6.620063224 Simplifying x = 6.620063224Subproblem 2
x + -1.875 = -4.745063224 Simplifying x + -1.875 = -4.745063224 Reorder the terms: -1.875 + x = -4.745063224 Solving -1.875 + x = -4.745063224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -4.745063224 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -4.745063224 + 1.875 x = -4.745063224 + 1.875 Combine like terms: -4.745063224 + 1.875 = -2.870063224 x = -2.870063224 Simplifying x = -2.870063224Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.620063224, -2.870063224}
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