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Simplifying 2x2 + 14x + -4 = -1x + 3 Reorder the terms: -4 + 14x + 2x2 = -1x + 3 Reorder the terms: -4 + 14x + 2x2 = 3 + -1x Solving -4 + 14x + 2x2 = 3 + -1x Solving for variable 'x'. Reorder the terms: -4 + -3 + 14x + x + 2x2 = 3 + -1x + -3 + x Combine like terms: -4 + -3 = -7 -7 + 14x + x + 2x2 = 3 + -1x + -3 + x Combine like terms: 14x + x = 15x -7 + 15x + 2x2 = 3 + -1x + -3 + x Reorder the terms: -7 + 15x + 2x2 = 3 + -3 + -1x + x Combine like terms: 3 + -3 = 0 -7 + 15x + 2x2 = 0 + -1x + x -7 + 15x + 2x2 = -1x + x Combine like terms: -1x + x = 0 -7 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 7.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 7.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 7.5x + x2 = 0 + 3.5 7.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 7.5x + x2 = 3.5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 3.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 3.5 + 14.0625 Combine like terms: 3.5 + 14.0625 = 17.5625 14.0625 + 7.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + 3.75) equal to 4.190763654 and -4.190763654.Subproblem 1
x + 3.75 = 4.190763654 Simplifying x + 3.75 = 4.190763654 Reorder the terms: 3.75 + x = 4.190763654 Solving 3.75 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 4.190763654 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.190763654 + -3.75 x = 4.190763654 + -3.75 Combine like terms: 4.190763654 + -3.75 = 0.440763654 x = 0.440763654 Simplifying x = 0.440763654Subproblem 2
x + 3.75 = -4.190763654 Simplifying x + 3.75 = -4.190763654 Reorder the terms: 3.75 + x = -4.190763654 Solving 3.75 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -4.190763654 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.190763654 + -3.75 x = -4.190763654 + -3.75 Combine like terms: -4.190763654 + -3.75 = -7.940763654 x = -7.940763654 Simplifying x = -7.940763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.440763654, -7.940763654}
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