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Simplifying 70 = (2x + 2)(x + 4) Reorder the terms: 70 = (2 + 2x)(x + 4) Reorder the terms: 70 = (2 + 2x)(4 + x) Multiply (2 + 2x) * (4 + x) 70 = (2(4 + x) + 2x * (4 + x)) 70 = ((4 * 2 + x * 2) + 2x * (4 + x)) 70 = ((8 + 2x) + 2x * (4 + x)) 70 = (8 + 2x + (4 * 2x + x * 2x)) 70 = (8 + 2x + (8x + 2x2)) Combine like terms: 2x + 8x = 10x 70 = (8 + 10x + 2x2) Solving 70 = 8 + 10x + 2x2 Solving for variable 'x'. Combine like terms: 70 + -8 = 62 62 + -10x + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2 Reorder the terms: 62 + -10x + -2x2 = 8 + -8 + 10x + -10x + 2x2 + -2x2 Combine like terms: 8 + -8 = 0 62 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2 62 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 62 + -10x + -2x2 = 0 + 2x2 + -2x2 62 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 62 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(31 + -5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 31 + -5x + -1x2 = 0 Solving 31 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + 5x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 5x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 5x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 5x + x2 = 0 + 31 5x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 5x + x2 = 31 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 31 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 31 + 6.25 Combine like terms: 31 + 6.25 = 37.25 6.25 + 5x + x2 = 37.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 2.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 2.5 = 6.103277808 Simplifying x + 2.5 = 6.103277808 Reorder the terms: 2.5 + x = 6.103277808 Solving 2.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.103277808 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.103277808 + -2.5 x = 6.103277808 + -2.5 Combine like terms: 6.103277808 + -2.5 = 3.603277808 x = 3.603277808 Simplifying x = 3.603277808Subproblem 2
x + 2.5 = -6.103277808 Simplifying x + 2.5 = -6.103277808 Reorder the terms: 2.5 + x = -6.103277808 Solving 2.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.103277808 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.103277808 + -2.5 x = -6.103277808 + -2.5 Combine like terms: -6.103277808 + -2.5 = -8.603277808 x = -8.603277808 Simplifying x = -8.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.603277808, -8.603277808}Solution
x = {3.603277808, -8.603277808}
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