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Simplifying 2x(x + -2) + -1(x + 4) = 28 Reorder the terms: 2x(-2 + x) + -1(x + 4) = 28 (-2 * 2x + x * 2x) + -1(x + 4) = 28 (-4x + 2x2) + -1(x + 4) = 28 Reorder the terms: -4x + 2x2 + -1(4 + x) = 28 -4x + 2x2 + (4 * -1 + x * -1) = 28 -4x + 2x2 + (-4 + -1x) = 28 Reorder the terms: -4 + -4x + -1x + 2x2 = 28 Combine like terms: -4x + -1x = -5x -4 + -5x + 2x2 = 28 Solving -4 + -5x + 2x2 = 28 Solving for variable 'x'. Reorder the terms: -4 + -28 + -5x + 2x2 = 28 + -28 Combine like terms: -4 + -28 = -32 -32 + -5x + 2x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -32 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16 + -2.5x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -2.5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -2.5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -2.5x + x2 = 0 + 16 -2.5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -2.5x + x2 = 16 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 16 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 16 + 1.5625 Combine like terms: 16 + 1.5625 = 17.5625 1.5625 + -2.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + -1.25) equal to 4.190763654 and -4.190763654.Subproblem 1
x + -1.25 = 4.190763654 Simplifying x + -1.25 = 4.190763654 Reorder the terms: -1.25 + x = 4.190763654 Solving -1.25 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 4.190763654 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.190763654 + 1.25 x = 4.190763654 + 1.25 Combine like terms: 4.190763654 + 1.25 = 5.440763654 x = 5.440763654 Simplifying x = 5.440763654Subproblem 2
x + -1.25 = -4.190763654 Simplifying x + -1.25 = -4.190763654 Reorder the terms: -1.25 + x = -4.190763654 Solving -1.25 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -4.190763654 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.190763654 + 1.25 x = -4.190763654 + 1.25 Combine like terms: -4.190763654 + 1.25 = -2.940763654 x = -2.940763654 Simplifying x = -2.940763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.440763654, -2.940763654}
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