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Simplifying 2x2 + -28x + 70 = 0 Reorder the terms: 70 + -28x + 2x2 = 0 Solving 70 + -28x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(35 + -14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + -14x + x2)' equal to zero and attempt to solve: Simplifying 35 + -14x + x2 = 0 Solving 35 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -14x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -14x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -14x + x2 = 0 + -35 -14x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -14x + x2 = -35 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 = -35 + 49 Reorder the terms: 49 + -14x + x2 = -35 + 49 Combine like terms: -35 + 49 = 14 49 + -14x + x2 = 14 Factor a perfect square on the left side: (x + -7)(x + -7) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -7) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -7 = 3.741657387 Simplifying x + -7 = 3.741657387 Reorder the terms: -7 + x = 3.741657387 Solving -7 + x = 3.741657387 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 = 3.741657387 + 7 Combine like terms: -7 + 7 = 0 0 + x = 3.741657387 + 7 x = 3.741657387 + 7 Combine like terms: 3.741657387 + 7 = 10.741657387 x = 10.741657387 Simplifying x = 10.741657387Subproblem 2
x + -7 = -3.741657387 Simplifying x + -7 = -3.741657387 Reorder the terms: -7 + x = -3.741657387 Solving -7 + x = -3.741657387 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 = -3.741657387 + 7 Combine like terms: -7 + 7 = 0 0 + x = -3.741657387 + 7 x = -3.741657387 + 7 Combine like terms: -3.741657387 + 7 = 3.258342613 x = 3.258342613 Simplifying x = 3.258342613Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.741657387, 3.258342613}Solution
x = {10.741657387, 3.258342613}
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