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Simplifying x = 4(9x2 + 16x + -40) Reorder the terms: x = 4(-40 + 16x + 9x2) x = (-40 * 4 + 16x * 4 + 9x2 * 4) x = (-160 + 64x + 36x2) Solving x = -160 + 64x + 36x2 Solving for variable 'x'. Reorder the terms: 160 + x + -64x + -36x2 = -160 + 64x + 36x2 + 160 + -64x + -36x2 Combine like terms: x + -64x = -63x 160 + -63x + -36x2 = -160 + 64x + 36x2 + 160 + -64x + -36x2 Reorder the terms: 160 + -63x + -36x2 = -160 + 160 + 64x + -64x + 36x2 + -36x2 Combine like terms: -160 + 160 = 0 160 + -63x + -36x2 = 0 + 64x + -64x + 36x2 + -36x2 160 + -63x + -36x2 = 64x + -64x + 36x2 + -36x2 Combine like terms: 64x + -64x = 0 160 + -63x + -36x2 = 0 + 36x2 + -36x2 160 + -63x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 160 + -63x + -36x2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. -4.444444444 + 1.75x + x2 = 0 Move the constant term to the right: Add '4.444444444' to each side of the equation. -4.444444444 + 1.75x + 4.444444444 + x2 = 0 + 4.444444444 Reorder the terms: -4.444444444 + 4.444444444 + 1.75x + x2 = 0 + 4.444444444 Combine like terms: -4.444444444 + 4.444444444 = 0.000000000 0.000000000 + 1.75x + x2 = 0 + 4.444444444 1.75x + x2 = 0 + 4.444444444 Combine like terms: 0 + 4.444444444 = 4.444444444 1.75x + x2 = 4.444444444 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 4.444444444 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 4.444444444 + 0.765625 Combine like terms: 4.444444444 + 0.765625 = 5.210069444 0.765625 + 1.75x + x2 = 5.210069444 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 5.210069444 Calculate the square root of the right side: 2.282557654 Break this problem into two subproblems by setting (x + 0.875) equal to 2.282557654 and -2.282557654.Subproblem 1
x + 0.875 = 2.282557654 Simplifying x + 0.875 = 2.282557654 Reorder the terms: 0.875 + x = 2.282557654 Solving 0.875 + x = 2.282557654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 2.282557654 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.282557654 + -0.875 x = 2.282557654 + -0.875 Combine like terms: 2.282557654 + -0.875 = 1.407557654 x = 1.407557654 Simplifying x = 1.407557654Subproblem 2
x + 0.875 = -2.282557654 Simplifying x + 0.875 = -2.282557654 Reorder the terms: 0.875 + x = -2.282557654 Solving 0.875 + x = -2.282557654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -2.282557654 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.282557654 + -0.875 x = -2.282557654 + -0.875 Combine like terms: -2.282557654 + -0.875 = -3.157557654 x = -3.157557654 Simplifying x = -3.157557654Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.407557654, -3.157557654}
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