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Simplifying 28x2 + -88x + 28 = 0 Reorder the terms: 28 + -88x + 28x2 = 0 Solving 28 + -88x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -22x + 7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -22x + 7x2)' equal to zero and attempt to solve: Simplifying 7 + -22x + 7x2 = 0 Solving 7 + -22x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + -3.142857143x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.142857143x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -3.142857143x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.142857143x + x2 = 0 + -1 -3.142857143x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.142857143x + x2 = -1 The x term is -3.142857143x. Take half its coefficient (-1.571428572). Square it (2.469387757) and add it to both sides. Add '2.469387757' to each side of the equation. -3.142857143x + 2.469387757 + x2 = -1 + 2.469387757 Reorder the terms: 2.469387757 + -3.142857143x + x2 = -1 + 2.469387757 Combine like terms: -1 + 2.469387757 = 1.469387757 2.469387757 + -3.142857143x + x2 = 1.469387757 Factor a perfect square on the left side: (x + -1.571428572)(x + -1.571428572) = 1.469387757 Calculate the square root of the right side: 1.212183054 Break this problem into two subproblems by setting (x + -1.571428572) equal to 1.212183054 and -1.212183054.Subproblem 1
x + -1.571428572 = 1.212183054 Simplifying x + -1.571428572 = 1.212183054 Reorder the terms: -1.571428572 + x = 1.212183054 Solving -1.571428572 + x = 1.212183054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.571428572' to each side of the equation. -1.571428572 + 1.571428572 + x = 1.212183054 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + x = 1.212183054 + 1.571428572 x = 1.212183054 + 1.571428572 Combine like terms: 1.212183054 + 1.571428572 = 2.783611626 x = 2.783611626 Simplifying x = 2.783611626Subproblem 2
x + -1.571428572 = -1.212183054 Simplifying x + -1.571428572 = -1.212183054 Reorder the terms: -1.571428572 + x = -1.212183054 Solving -1.571428572 + x = -1.212183054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.571428572' to each side of the equation. -1.571428572 + 1.571428572 + x = -1.212183054 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + x = -1.212183054 + 1.571428572 x = -1.212183054 + 1.571428572 Combine like terms: -1.212183054 + 1.571428572 = 0.359245518 x = 0.359245518 Simplifying x = 0.359245518Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.783611626, 0.359245518}Solution
x = {2.783611626, 0.359245518}
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