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Simplifying 2x2 + -9x + -14 = 4x Reorder the terms: -14 + -9x + 2x2 = 4x Solving -14 + -9x + 2x2 = 4x Solving for variable 'x'. Reorder the terms: -14 + -9x + -4x + 2x2 = 4x + -4x Combine like terms: -9x + -4x = -13x -14 + -13x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -14 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + -6.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -6.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -6.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6.5x + x2 = 0 + 7 -6.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -6.5x + x2 = 7 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 7 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 7 + 10.5625 Combine like terms: 7 + 10.5625 = 17.5625 10.5625 + -6.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + -3.25) equal to 4.190763654 and -4.190763654.Subproblem 1
x + -3.25 = 4.190763654 Simplifying x + -3.25 = 4.190763654 Reorder the terms: -3.25 + x = 4.190763654 Solving -3.25 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.190763654 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.190763654 + 3.25 x = 4.190763654 + 3.25 Combine like terms: 4.190763654 + 3.25 = 7.440763654 x = 7.440763654 Simplifying x = 7.440763654Subproblem 2
x + -3.25 = -4.190763654 Simplifying x + -3.25 = -4.190763654 Reorder the terms: -3.25 + x = -4.190763654 Solving -3.25 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.190763654 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.190763654 + 3.25 x = -4.190763654 + 3.25 Combine like terms: -4.190763654 + 3.25 = -0.940763654 x = -0.940763654 Simplifying x = -0.940763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.440763654, -0.940763654}
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