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Simplifying (4x + 3)(4x + 3) = 10 Reorder the terms: (3 + 4x)(4x + 3) = 10 Reorder the terms: (3 + 4x)(3 + 4x) = 10 Multiply (3 + 4x) * (3 + 4x) (3(3 + 4x) + 4x * (3 + 4x)) = 10 ((3 * 3 + 4x * 3) + 4x * (3 + 4x)) = 10 ((9 + 12x) + 4x * (3 + 4x)) = 10 (9 + 12x + (3 * 4x + 4x * 4x)) = 10 (9 + 12x + (12x + 16x2)) = 10 Combine like terms: 12x + 12x = 24x (9 + 24x + 16x2) = 10 Solving 9 + 24x + 16x2 = 10 Solving for variable 'x'. Reorder the terms: 9 + -10 + 24x + 16x2 = 10 + -10 Combine like terms: 9 + -10 = -1 -1 + 24x + 16x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -1 + 24x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + 1.5x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 1.5x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 1.5x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 1.5x + x2 = 0 + 0.0625 1.5x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 1.5x + x2 = 0.0625 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 0.0625 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.0625 + 0.5625 Combine like terms: 0.0625 + 0.5625 = 0.625 0.5625 + 1.5x + x2 = 0.625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (x + 0.75) equal to 0.790569415 and -0.790569415.Subproblem 1
x + 0.75 = 0.790569415 Simplifying x + 0.75 = 0.790569415 Reorder the terms: 0.75 + x = 0.790569415 Solving 0.75 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.790569415 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.790569415 + -0.75 x = 0.790569415 + -0.75 Combine like terms: 0.790569415 + -0.75 = 0.040569415 x = 0.040569415 Simplifying x = 0.040569415Subproblem 2
x + 0.75 = -0.790569415 Simplifying x + 0.75 = -0.790569415 Reorder the terms: 0.75 + x = -0.790569415 Solving 0.75 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -0.790569415 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.790569415 + -0.75 x = -0.790569415 + -0.75 Combine like terms: -0.790569415 + -0.75 = -1.540569415 x = -1.540569415 Simplifying x = -1.540569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.040569415, -1.540569415}
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