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Simplifying 2x2 + 3x + -110 = 0 Reorder the terms: -110 + 3x + 2x2 = 0 Solving -110 + 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'. -55 + 1.5x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + 1.5x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 1.5x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 1.5x + x2 = 0 + 55 1.5x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 1.5x + x2 = 55 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 = 55 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 55 + 0.5625 Combine like terms: 55 + 0.5625 = 55.5625 0.5625 + 1.5x + x2 = 55.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 55.5625 Calculate the square root of the right side: 7.454025758 Break this problem into two subproblems by setting (x + 0.75) equal to 7.454025758 and -7.454025758.Subproblem 1
x + 0.75 = 7.454025758 Simplifying x + 0.75 = 7.454025758 Reorder the terms: 0.75 + x = 7.454025758 Solving 0.75 + x = 7.454025758 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 = 7.454025758 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.454025758 + -0.75 x = 7.454025758 + -0.75 Combine like terms: 7.454025758 + -0.75 = 6.704025758 x = 6.704025758 Simplifying x = 6.704025758Subproblem 2
x + 0.75 = -7.454025758 Simplifying x + 0.75 = -7.454025758 Reorder the terms: 0.75 + x = -7.454025758 Solving 0.75 + x = -7.454025758 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 = -7.454025758 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.454025758 + -0.75 x = -7.454025758 + -0.75 Combine like terms: -7.454025758 + -0.75 = -8.204025758 x = -8.204025758 Simplifying x = -8.204025758Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.704025758, -8.204025758}
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