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Simplifying 2x2 + 3x + -114 = 0 Reorder the terms: -114 + 3x + 2x2 = 0 Solving -114 + 3x + 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'. -57 + 1.5x + x2 = 0 Move the constant term to the right: Add '57' to each side of the equation. -57 + 1.5x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + 1.5x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + 1.5x + x2 = 0 + 57 1.5x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 1.5x + x2 = 57 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 57 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 57 + 0.5625 Combine like terms: 57 + 0.5625 = 57.5625 0.5625 + 1.5x + x2 = 57.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 57.5625 Calculate the square root of the right side: 7.586995453 Break this problem into two subproblems by setting (x + 0.75) equal to 7.586995453 and -7.586995453.Subproblem 1
x + 0.75 = 7.586995453 Simplifying x + 0.75 = 7.586995453 Reorder the terms: 0.75 + x = 7.586995453 Solving 0.75 + x = 7.586995453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 7.586995453 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.586995453 + -0.75 x = 7.586995453 + -0.75 Combine like terms: 7.586995453 + -0.75 = 6.836995453 x = 6.836995453 Simplifying x = 6.836995453Subproblem 2
x + 0.75 = -7.586995453 Simplifying x + 0.75 = -7.586995453 Reorder the terms: 0.75 + x = -7.586995453 Solving 0.75 + x = -7.586995453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -7.586995453 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.586995453 + -0.75 x = -7.586995453 + -0.75 Combine like terms: -7.586995453 + -0.75 = -8.336995453 x = -8.336995453 Simplifying x = -8.336995453Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.836995453, -8.336995453}
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