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Simplifying 0 = -40(x2 + -14x + 20) Reorder the terms: 0 = -40(20 + -14x + x2) 0 = (20 * -40 + -14x * -40 + x2 * -40) 0 = (-800 + 560x + -40x2) Solving 0 = -800 + 560x + -40x2 Solving for variable 'x'. Combine like terms: 0 + 800 = 800 800 + -560x + 40x2 = -800 + 560x + -40x2 + 800 + -560x + 40x2 Reorder the terms: 800 + -560x + 40x2 = -800 + 800 + 560x + -560x + -40x2 + 40x2 Combine like terms: -800 + 800 = 0 800 + -560x + 40x2 = 0 + 560x + -560x + -40x2 + 40x2 800 + -560x + 40x2 = 560x + -560x + -40x2 + 40x2 Combine like terms: 560x + -560x = 0 800 + -560x + 40x2 = 0 + -40x2 + 40x2 800 + -560x + 40x2 = -40x2 + 40x2 Combine like terms: -40x2 + 40x2 = 0 800 + -560x + 40x2 = 0 Factor out the Greatest Common Factor (GCF), '40'. 40(20 + -14x + x2) = 0 Ignore the factor 40.Subproblem 1
Set the factor '(20 + -14x + x2)' equal to zero and attempt to solve: Simplifying 20 + -14x + x2 = 0 Solving 20 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -14x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -14x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -14x + x2 = 0 + -20 -14x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -14x + x2 = -20 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -20 + 49 Reorder the terms: 49 + -14x + x2 = -20 + 49 Combine like terms: -20 + 49 = 29 49 + -14x + x2 = 29 Factor a perfect square on the left side: (x + -7)(x + -7) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -7) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -7 = 5.385164807 Simplifying x + -7 = 5.385164807 Reorder the terms: -7 + x = 5.385164807 Solving -7 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 5.385164807 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.385164807 + 7 x = 5.385164807 + 7 Combine like terms: 5.385164807 + 7 = 12.385164807 x = 12.385164807 Simplifying x = 12.385164807Subproblem 2
x + -7 = -5.385164807 Simplifying x + -7 = -5.385164807 Reorder the terms: -7 + x = -5.385164807 Solving -7 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -5.385164807 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.385164807 + 7 x = -5.385164807 + 7 Combine like terms: -5.385164807 + 7 = 1.614835193 x = 1.614835193 Simplifying x = 1.614835193Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.385164807, 1.614835193}Solution
x = {12.385164807, 1.614835193}
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