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Simplifying 5x + -1[21 + -1(3 + -11) * x] * x = -2 Combine like terms: 3 + -11 = -8 5x + -1[21 + -1(-8) * x] * x = -2 Multiply -1 * -8 5x + -1[21 + 8x] * x = -2 Reorder the terms for easier multiplication: 5x + -1x[21 + 8x] = -2 5x + [21 * -1x + 8x * -1x] = -2 5x + [-21x + -8x2] = -2 Combine like terms: 5x + -21x = -16x -16x + -8x2 = -2 Solving -16x + -8x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + -16x + -8x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -16x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -8x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -8x + -4x2)' equal to zero and attempt to solve: Simplifying 1 + -8x + -4x2 = 0 Solving 1 + -8x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + 2x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 2x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 2x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 2x + x2 = 0 + 0.25 2x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 2x + x2 = 0.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.25 + 1 Reorder the terms: 1 + 2x + x2 = 0.25 + 1 Combine like terms: 0.25 + 1 = 1.25 1 + 2x + x2 = 1.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 1) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 1 = 1.118033989 Simplifying x + 1 = 1.118033989 Reorder the terms: 1 + x = 1.118033989 Solving 1 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.118033989 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.118033989 + -1 x = 1.118033989 + -1 Combine like terms: 1.118033989 + -1 = 0.118033989 x = 0.118033989 Simplifying x = 0.118033989Subproblem 2
x + 1 = -1.118033989 Simplifying x + 1 = -1.118033989 Reorder the terms: 1 + x = -1.118033989 Solving 1 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.118033989 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.118033989 + -1 x = -1.118033989 + -1 Combine like terms: -1.118033989 + -1 = -2.118033989 x = -2.118033989 Simplifying x = -2.118033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.118033989, -2.118033989}Solution
x = {0.118033989, -2.118033989}
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