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Simplifying 1 + -5x = (x + -1)(4x + 7) Reorder the terms: 1 + -5x = (-1 + x)(4x + 7) Reorder the terms: 1 + -5x = (-1 + x)(7 + 4x) Multiply (-1 + x) * (7 + 4x) 1 + -5x = (-1(7 + 4x) + x(7 + 4x)) 1 + -5x = ((7 * -1 + 4x * -1) + x(7 + 4x)) 1 + -5x = ((-7 + -4x) + x(7 + 4x)) 1 + -5x = (-7 + -4x + (7 * x + 4x * x)) 1 + -5x = (-7 + -4x + (7x + 4x2)) Combine like terms: -4x + 7x = 3x 1 + -5x = (-7 + 3x + 4x2) Solving 1 + -5x = -7 + 3x + 4x2 Solving for variable 'x'. Reorder the terms: 1 + 7 + -5x + -3x + -4x2 = -7 + 3x + 4x2 + 7 + -3x + -4x2 Combine like terms: 1 + 7 = 8 8 + -5x + -3x + -4x2 = -7 + 3x + 4x2 + 7 + -3x + -4x2 Combine like terms: -5x + -3x = -8x 8 + -8x + -4x2 = -7 + 3x + 4x2 + 7 + -3x + -4x2 Reorder the terms: 8 + -8x + -4x2 = -7 + 7 + 3x + -3x + 4x2 + -4x2 Combine like terms: -7 + 7 = 0 8 + -8x + -4x2 = 0 + 3x + -3x + 4x2 + -4x2 8 + -8x + -4x2 = 3x + -3x + 4x2 + -4x2 Combine like terms: 3x + -3x = 0 8 + -8x + -4x2 = 0 + 4x2 + -4x2 8 + -8x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 8 + -8x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -2x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -2x + -1x2 = 0 Solving 2 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 2x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2x + x2 = 0 + 2 2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2x + x2 = 2 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 = 2 + 1 Reorder the terms: 1 + 2x + x2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + 2x + x2 = 3 Factor a perfect square on the left side: (x + 1)(x + 1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 1) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 1 = 1.732050808 Simplifying x + 1 = 1.732050808 Reorder the terms: 1 + x = 1.732050808 Solving 1 + x = 1.732050808 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 = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.732050808 + -1 x = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 x = 0.732050808 Simplifying x = 0.732050808Subproblem 2
x + 1 = -1.732050808 Simplifying x + 1 = -1.732050808 Reorder the terms: 1 + x = -1.732050808 Solving 1 + x = -1.732050808 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 = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.732050808 + -1 x = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 x = -2.732050808 Simplifying x = -2.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.732050808, -2.732050808}Solution
x = {0.732050808, -2.732050808}
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