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Simplifying 2x2 + -28x + 84 = 0 Reorder the terms: 84 + -28x + 2x2 = 0 Solving 84 + -28x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(42 + -14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(42 + -14x + x2)' equal to zero and attempt to solve: Simplifying 42 + -14x + x2 = 0 Solving 42 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -14x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -14x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -14x + x2 = 0 + -42 -14x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -14x + x2 = -42 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 = -42 + 49 Reorder the terms: 49 + -14x + x2 = -42 + 49 Combine like terms: -42 + 49 = 7 49 + -14x + x2 = 7 Factor a perfect square on the left side: (x + -7)(x + -7) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -7) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -7 = 2.645751311 Simplifying x + -7 = 2.645751311 Reorder the terms: -7 + x = 2.645751311 Solving -7 + x = 2.645751311 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 = 2.645751311 + 7 Combine like terms: -7 + 7 = 0 0 + x = 2.645751311 + 7 x = 2.645751311 + 7 Combine like terms: 2.645751311 + 7 = 9.645751311 x = 9.645751311 Simplifying x = 9.645751311Subproblem 2
x + -7 = -2.645751311 Simplifying x + -7 = -2.645751311 Reorder the terms: -7 + x = -2.645751311 Solving -7 + x = -2.645751311 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 = -2.645751311 + 7 Combine like terms: -7 + 7 = 0 0 + x = -2.645751311 + 7 x = -2.645751311 + 7 Combine like terms: -2.645751311 + 7 = 4.354248689 x = 4.354248689 Simplifying x = 4.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.645751311, 4.354248689}Solution
x = {9.645751311, 4.354248689}
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