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Simplifying (2x + 5)(x + -5) + -7 = 0 Reorder the terms: (5 + 2x)(x + -5) + -7 = 0 Reorder the terms: (5 + 2x)(-5 + x) + -7 = 0 Multiply (5 + 2x) * (-5 + x) (5(-5 + x) + 2x * (-5 + x)) + -7 = 0 ((-5 * 5 + x * 5) + 2x * (-5 + x)) + -7 = 0 ((-25 + 5x) + 2x * (-5 + x)) + -7 = 0 (-25 + 5x + (-5 * 2x + x * 2x)) + -7 = 0 (-25 + 5x + (-10x + 2x2)) + -7 = 0 Combine like terms: 5x + -10x = -5x (-25 + -5x + 2x2) + -7 = 0 Reorder the terms: -25 + -7 + -5x + 2x2 = 0 Combine like terms: -25 + -7 = -32 -32 + -5x + 2x2 = 0 Solving -32 + -5x + 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'. -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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