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Simplifying 2x2 + 3x + -34 = 0 Reorder the terms: -34 + 3x + 2x2 = 0 Solving -34 + 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'. -17 + 1.5x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 1.5x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 1.5x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 1.5x + x2 = 0 + 17 1.5x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 1.5x + x2 = 17 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 = 17 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 17 + 0.5625 Combine like terms: 17 + 0.5625 = 17.5625 0.5625 + 1.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + 0.75) equal to 4.190763654 and -4.190763654.Subproblem 1
x + 0.75 = 4.190763654 Simplifying x + 0.75 = 4.190763654 Reorder the terms: 0.75 + x = 4.190763654 Solving 0.75 + x = 4.190763654 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 = 4.190763654 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.190763654 + -0.75 x = 4.190763654 + -0.75 Combine like terms: 4.190763654 + -0.75 = 3.440763654 x = 3.440763654 Simplifying x = 3.440763654Subproblem 2
x + 0.75 = -4.190763654 Simplifying x + 0.75 = -4.190763654 Reorder the terms: 0.75 + x = -4.190763654 Solving 0.75 + x = -4.190763654 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 = -4.190763654 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.190763654 + -0.75 x = -4.190763654 + -0.75 Combine like terms: -4.190763654 + -0.75 = -4.940763654 x = -4.940763654 Simplifying x = -4.940763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.440763654, -4.940763654}
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