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Simplifying 4(x2 + 20x + 25) = -2 Reorder the terms: 4(25 + 20x + x2) = -2 (25 * 4 + 20x * 4 + x2 * 4) = -2 (100 + 80x + 4x2) = -2 Solving 100 + 80x + 4x2 = -2 Solving for variable 'x'. Reorder the terms: 100 + 2 + 80x + 4x2 = -2 + 2 Combine like terms: 100 + 2 = 102 102 + 80x + 4x2 = -2 + 2 Combine like terms: -2 + 2 = 0 102 + 80x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(51 + 40x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(51 + 40x + 2x2)' equal to zero and attempt to solve: Simplifying 51 + 40x + 2x2 = 0 Solving 51 + 40x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 25.5 + 20x + x2 = 0 Move the constant term to the right: Add '-25.5' to each side of the equation. 25.5 + 20x + -25.5 + x2 = 0 + -25.5 Reorder the terms: 25.5 + -25.5 + 20x + x2 = 0 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + 20x + x2 = 0 + -25.5 20x + x2 = 0 + -25.5 Combine like terms: 0 + -25.5 = -25.5 20x + x2 = -25.5 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -25.5 + 100 Reorder the terms: 100 + 20x + x2 = -25.5 + 100 Combine like terms: -25.5 + 100 = 74.5 100 + 20x + x2 = 74.5 Factor a perfect square on the left side: (x + 10)(x + 10) = 74.5 Calculate the square root of the right side: 8.631338251 Break this problem into two subproblems by setting (x + 10) equal to 8.631338251 and -8.631338251.Subproblem 1
x + 10 = 8.631338251 Simplifying x + 10 = 8.631338251 Reorder the terms: 10 + x = 8.631338251 Solving 10 + x = 8.631338251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 8.631338251 + -10 Combine like terms: 10 + -10 = 0 0 + x = 8.631338251 + -10 x = 8.631338251 + -10 Combine like terms: 8.631338251 + -10 = -1.368661749 x = -1.368661749 Simplifying x = -1.368661749Subproblem 2
x + 10 = -8.631338251 Simplifying x + 10 = -8.631338251 Reorder the terms: 10 + x = -8.631338251 Solving 10 + x = -8.631338251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -8.631338251 + -10 Combine like terms: 10 + -10 = 0 0 + x = -8.631338251 + -10 x = -8.631338251 + -10 Combine like terms: -8.631338251 + -10 = -18.631338251 x = -18.631338251 Simplifying x = -18.631338251Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.368661749, -18.631338251}Solution
x = {-1.368661749, -18.631338251}
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