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Simplifying 4x2 + 7x = 480 Reorder the terms: 7x + 4x2 = 480 Solving 7x + 4x2 = 480 Solving for variable 'x'. Reorder the terms: -480 + 7x + 4x2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -120 + 1.75x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 1.75x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 1.75x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 1.75x + x2 = 0 + 120 1.75x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 1.75x + x2 = 120 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 = 120 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 120 + 0.765625 Combine like terms: 120 + 0.765625 = 120.765625 0.765625 + 1.75x + x2 = 120.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 120.765625 Calculate the square root of the right side: 10.989341427 Break this problem into two subproblems by setting (x + 0.875) equal to 10.989341427 and -10.989341427.Subproblem 1
x + 0.875 = 10.989341427 Simplifying x + 0.875 = 10.989341427 Reorder the terms: 0.875 + x = 10.989341427 Solving 0.875 + x = 10.989341427 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 = 10.989341427 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 10.989341427 + -0.875 x = 10.989341427 + -0.875 Combine like terms: 10.989341427 + -0.875 = 10.114341427 x = 10.114341427 Simplifying x = 10.114341427Subproblem 2
x + 0.875 = -10.989341427 Simplifying x + 0.875 = -10.989341427 Reorder the terms: 0.875 + x = -10.989341427 Solving 0.875 + x = -10.989341427 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 = -10.989341427 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -10.989341427 + -0.875 x = -10.989341427 + -0.875 Combine like terms: -10.989341427 + -0.875 = -11.864341427 x = -11.864341427 Simplifying x = -11.864341427Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.114341427, -11.864341427}
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