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Simplifying 3[(x + 5)(x + 5)] = 21 Reorder the terms: 3[(5 + x)(x + 5)] = 21 Reorder the terms: 3[(5 + x)(5 + x)] = 21 Multiply (5 + x) * (5 + x) 3[(5(5 + x) + x(5 + x))] = 21 3[((5 * 5 + x * 5) + x(5 + x))] = 21 3[((25 + 5x) + x(5 + x))] = 21 3[(25 + 5x + (5 * x + x * x))] = 21 3[(25 + 5x + (5x + x2))] = 21 Combine like terms: 5x + 5x = 10x 3[(25 + 10x + x2)] = 21 [25 * 3 + 10x * 3 + x2 * 3] = 21 [75 + 30x + 3x2] = 21 Solving 75 + 30x + 3x2 = 21 Solving for variable 'x'. Reorder the terms: 75 + -21 + 30x + 3x2 = 21 + -21 Combine like terms: 75 + -21 = 54 54 + 30x + 3x2 = 21 + -21 Combine like terms: 21 + -21 = 0 54 + 30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(18 + 10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(18 + 10x + x2)' equal to zero and attempt to solve: Simplifying 18 + 10x + x2 = 0 Solving 18 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 10x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 10x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 10x + x2 = 0 + -18 10x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 10x + x2 = -18 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -18 + 25 Reorder the terms: 25 + 10x + x2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + 10x + x2 = 7 Factor a perfect square on the left side: (x + 5)(x + 5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 5) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 5 = 2.645751311 Simplifying x + 5 = 2.645751311 Reorder the terms: 5 + x = 2.645751311 Solving 5 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + x = 2.645751311 + -5 x = 2.645751311 + -5 Combine like terms: 2.645751311 + -5 = -2.354248689 x = -2.354248689 Simplifying x = -2.354248689Subproblem 2
x + 5 = -2.645751311 Simplifying x + 5 = -2.645751311 Reorder the terms: 5 + x = -2.645751311 Solving 5 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + x = -2.645751311 + -5 x = -2.645751311 + -5 Combine like terms: -2.645751311 + -5 = -7.645751311 x = -7.645751311 Simplifying x = -7.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.354248689, -7.645751311}Solution
x = {-2.354248689, -7.645751311}
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