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Simplifying (4x2 + 2) + (7x + 3) = 71 Reorder the terms: (2 + 4x2) + (7x + 3) = 71 Remove parenthesis around (2 + 4x2) 2 + 4x2 + (7x + 3) = 71 Reorder the terms: 2 + 4x2 + (3 + 7x) = 71 Remove parenthesis around (3 + 7x) 2 + 4x2 + 3 + 7x = 71 Reorder the terms: 2 + 3 + 7x + 4x2 = 71 Combine like terms: 2 + 3 = 5 5 + 7x + 4x2 = 71 Solving 5 + 7x + 4x2 = 71 Solving for variable 'x'. Reorder the terms: 5 + -71 + 7x + 4x2 = 71 + -71 Combine like terms: 5 + -71 = -66 -66 + 7x + 4x2 = 71 + -71 Combine like terms: 71 + -71 = 0 -66 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -16.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 1.75x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 1.75x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 1.75x + x2 = 0 + 16.5 1.75x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 1.75x + x2 = 16.5 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 = 16.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 16.5 + 0.765625 Combine like terms: 16.5 + 0.765625 = 17.265625 0.765625 + 1.75x + x2 = 17.265625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 17.265625 Calculate the square root of the right side: 4.155192535 Break this problem into two subproblems by setting (x + 0.875) equal to 4.155192535 and -4.155192535.Subproblem 1
x + 0.875 = 4.155192535 Simplifying x + 0.875 = 4.155192535 Reorder the terms: 0.875 + x = 4.155192535 Solving 0.875 + x = 4.155192535 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 = 4.155192535 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 4.155192535 + -0.875 x = 4.155192535 + -0.875 Combine like terms: 4.155192535 + -0.875 = 3.280192535 x = 3.280192535 Simplifying x = 3.280192535Subproblem 2
x + 0.875 = -4.155192535 Simplifying x + 0.875 = -4.155192535 Reorder the terms: 0.875 + x = -4.155192535 Solving 0.875 + x = -4.155192535 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 = -4.155192535 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -4.155192535 + -0.875 x = -4.155192535 + -0.875 Combine like terms: -4.155192535 + -0.875 = -5.030192535 x = -5.030192535 Simplifying x = -5.030192535Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.280192535, -5.030192535}
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