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Simplifying (4x + 7)(4x + 7) = 10 Reorder the terms: (7 + 4x)(4x + 7) = 10 Reorder the terms: (7 + 4x)(7 + 4x) = 10 Multiply (7 + 4x) * (7 + 4x) (7(7 + 4x) + 4x * (7 + 4x)) = 10 ((7 * 7 + 4x * 7) + 4x * (7 + 4x)) = 10 ((49 + 28x) + 4x * (7 + 4x)) = 10 (49 + 28x + (7 * 4x + 4x * 4x)) = 10 (49 + 28x + (28x + 16x2)) = 10 Combine like terms: 28x + 28x = 56x (49 + 56x + 16x2) = 10 Solving 49 + 56x + 16x2 = 10 Solving for variable 'x'. Reorder the terms: 49 + -10 + 56x + 16x2 = 10 + -10 Combine like terms: 49 + -10 = 39 39 + 56x + 16x2 = 10 + -10 Combine like terms: 10 + -10 = 0 39 + 56x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.4375 + 3.5x + x2 = 0 Move the constant term to the right: Add '-2.4375' to each side of the equation. 2.4375 + 3.5x + -2.4375 + x2 = 0 + -2.4375 Reorder the terms: 2.4375 + -2.4375 + 3.5x + x2 = 0 + -2.4375 Combine like terms: 2.4375 + -2.4375 = 0.0000 0.0000 + 3.5x + x2 = 0 + -2.4375 3.5x + x2 = 0 + -2.4375 Combine like terms: 0 + -2.4375 = -2.4375 3.5x + x2 = -2.4375 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -2.4375 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -2.4375 + 3.0625 Combine like terms: -2.4375 + 3.0625 = 0.625 3.0625 + 3.5x + x2 = 0.625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (x + 1.75) equal to 0.790569415 and -0.790569415.Subproblem 1
x + 1.75 = 0.790569415 Simplifying x + 1.75 = 0.790569415 Reorder the terms: 1.75 + x = 0.790569415 Solving 1.75 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 0.790569415 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 0.790569415 + -1.75 x = 0.790569415 + -1.75 Combine like terms: 0.790569415 + -1.75 = -0.959430585 x = -0.959430585 Simplifying x = -0.959430585Subproblem 2
x + 1.75 = -0.790569415 Simplifying x + 1.75 = -0.790569415 Reorder the terms: 1.75 + x = -0.790569415 Solving 1.75 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -0.790569415 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -0.790569415 + -1.75 x = -0.790569415 + -1.75 Combine like terms: -0.790569415 + -1.75 = -2.540569415 x = -2.540569415 Simplifying x = -2.540569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.959430585, -2.540569415}
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