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Simplifying 70 = (2x + 4)(x + 5) Reorder the terms: 70 = (4 + 2x)(x + 5) Reorder the terms: 70 = (4 + 2x)(5 + x) Multiply (4 + 2x) * (5 + x) 70 = (4(5 + x) + 2x * (5 + x)) 70 = ((5 * 4 + x * 4) + 2x * (5 + x)) 70 = ((20 + 4x) + 2x * (5 + x)) 70 = (20 + 4x + (5 * 2x + x * 2x)) 70 = (20 + 4x + (10x + 2x2)) Combine like terms: 4x + 10x = 14x 70 = (20 + 14x + 2x2) Solving 70 = 20 + 14x + 2x2 Solving for variable 'x'. Combine like terms: 70 + -20 = 50 50 + -14x + -2x2 = 20 + 14x + 2x2 + -20 + -14x + -2x2 Reorder the terms: 50 + -14x + -2x2 = 20 + -20 + 14x + -14x + 2x2 + -2x2 Combine like terms: 20 + -20 = 0 50 + -14x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2 50 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 50 + -14x + -2x2 = 0 + 2x2 + -2x2 50 + -14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 50 + -14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 25 + -7x + -1x2 = 0 Solving 25 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 7x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 7x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 7x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 7x + x2 = 0 + 25 7x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 7x + x2 = 25 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 25 + 12.25 Combine like terms: 25 + 12.25 = 37.25 12.25 + 7x + x2 = 37.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 3.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 3.5 = 6.103277808 Simplifying x + 3.5 = 6.103277808 Reorder the terms: 3.5 + x = 6.103277808 Solving 3.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.103277808 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.103277808 + -3.5 x = 6.103277808 + -3.5 Combine like terms: 6.103277808 + -3.5 = 2.603277808 x = 2.603277808 Simplifying x = 2.603277808Subproblem 2
x + 3.5 = -6.103277808 Simplifying x + 3.5 = -6.103277808 Reorder the terms: 3.5 + x = -6.103277808 Solving 3.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.103277808 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.103277808 + -3.5 x = -6.103277808 + -3.5 Combine like terms: -6.103277808 + -3.5 = -9.603277808 x = -9.603277808 Simplifying x = -9.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.603277808, -9.603277808}Solution
x = {2.603277808, -9.603277808}
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