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Simplifying 2x2 + 3x + -91 = 0 Reorder the terms: -91 + 3x + 2x2 = 0 Solving -91 + 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'. -45.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '45.5' to each side of the equation. -45.5 + 1.5x + 45.5 + x2 = 0 + 45.5 Reorder the terms: -45.5 + 45.5 + 1.5x + x2 = 0 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + 1.5x + x2 = 0 + 45.5 1.5x + x2 = 0 + 45.5 Combine like terms: 0 + 45.5 = 45.5 1.5x + x2 = 45.5 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 = 45.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 45.5 + 0.5625 Combine like terms: 45.5 + 0.5625 = 46.0625 0.5625 + 1.5x + x2 = 46.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 46.0625 Calculate the square root of the right side: 6.78693598 Break this problem into two subproblems by setting (x + 0.75) equal to 6.78693598 and -6.78693598.Subproblem 1
x + 0.75 = 6.78693598 Simplifying x + 0.75 = 6.78693598 Reorder the terms: 0.75 + x = 6.78693598 Solving 0.75 + x = 6.78693598 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 = 6.78693598 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 6.78693598 + -0.75 x = 6.78693598 + -0.75 Combine like terms: 6.78693598 + -0.75 = 6.03693598 x = 6.03693598 Simplifying x = 6.03693598Subproblem 2
x + 0.75 = -6.78693598 Simplifying x + 0.75 = -6.78693598 Reorder the terms: 0.75 + x = -6.78693598 Solving 0.75 + x = -6.78693598 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 = -6.78693598 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -6.78693598 + -0.75 x = -6.78693598 + -0.75 Combine like terms: -6.78693598 + -0.75 = -7.53693598 x = -7.53693598 Simplifying x = -7.53693598Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.03693598, -7.53693598}
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