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Simplifying 4(x + 7)(x + 7) = 11 Reorder the terms: 4(7 + x)(x + 7) = 11 Reorder the terms: 4(7 + x)(7 + x) = 11 Multiply (7 + x) * (7 + x) 4(7(7 + x) + x(7 + x)) = 11 4((7 * 7 + x * 7) + x(7 + x)) = 11 4((49 + 7x) + x(7 + x)) = 11 4(49 + 7x + (7 * x + x * x)) = 11 4(49 + 7x + (7x + x2)) = 11 Combine like terms: 7x + 7x = 14x 4(49 + 14x + x2) = 11 (49 * 4 + 14x * 4 + x2 * 4) = 11 (196 + 56x + 4x2) = 11 Solving 196 + 56x + 4x2 = 11 Solving for variable 'x'. Reorder the terms: 196 + -11 + 56x + 4x2 = 11 + -11 Combine like terms: 196 + -11 = 185 185 + 56x + 4x2 = 11 + -11 Combine like terms: 11 + -11 = 0 185 + 56x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 46.25 + 14x + x2 = 0 Move the constant term to the right: Add '-46.25' to each side of the equation. 46.25 + 14x + -46.25 + x2 = 0 + -46.25 Reorder the terms: 46.25 + -46.25 + 14x + x2 = 0 + -46.25 Combine like terms: 46.25 + -46.25 = 0.00 0.00 + 14x + x2 = 0 + -46.25 14x + x2 = 0 + -46.25 Combine like terms: 0 + -46.25 = -46.25 14x + x2 = -46.25 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -46.25 + 49 Reorder the terms: 49 + 14x + x2 = -46.25 + 49 Combine like terms: -46.25 + 49 = 2.75 49 + 14x + x2 = 2.75 Factor a perfect square on the left side: (x + 7)(x + 7) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + 7) equal to 1.658312395 and -1.658312395.Subproblem 1
x + 7 = 1.658312395 Simplifying x + 7 = 1.658312395 Reorder the terms: 7 + x = 1.658312395 Solving 7 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 1.658312395 + -7 Combine like terms: 7 + -7 = 0 0 + x = 1.658312395 + -7 x = 1.658312395 + -7 Combine like terms: 1.658312395 + -7 = -5.341687605 x = -5.341687605 Simplifying x = -5.341687605Subproblem 2
x + 7 = -1.658312395 Simplifying x + 7 = -1.658312395 Reorder the terms: 7 + x = -1.658312395 Solving 7 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -1.658312395 + -7 Combine like terms: 7 + -7 = 0 0 + x = -1.658312395 + -7 x = -1.658312395 + -7 Combine like terms: -1.658312395 + -7 = -8.658312395 x = -8.658312395 Simplifying x = -8.658312395Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.341687605, -8.658312395}
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