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Simplifying 4x2 + -56x + 2 = 14 Reorder the terms: 2 + -56x + 4x2 = 14 Solving 2 + -56x + 4x2 = 14 Solving for variable 'x'. Reorder the terms: 2 + -14 + -56x + 4x2 = 14 + -14 Combine like terms: 2 + -14 = -12 -12 + -56x + 4x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -12 + -56x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -14x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -14x + x2)' equal to zero and attempt to solve: Simplifying -3 + -14x + x2 = 0 Solving -3 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -14x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -14x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -14x + x2 = 0 + 3 -14x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -14x + x2 = 3 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 = 3 + 49 Reorder the terms: 49 + -14x + x2 = 3 + 49 Combine like terms: 3 + 49 = 52 49 + -14x + x2 = 52 Factor a perfect square on the left side: (x + -7)(x + -7) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + -7) equal to 7.211102551 and -7.211102551.Subproblem 1
x + -7 = 7.211102551 Simplifying x + -7 = 7.211102551 Reorder the terms: -7 + x = 7.211102551 Solving -7 + x = 7.211102551 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 = 7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.211102551 + 7 x = 7.211102551 + 7 Combine like terms: 7.211102551 + 7 = 14.211102551 x = 14.211102551 Simplifying x = 14.211102551Subproblem 2
x + -7 = -7.211102551 Simplifying x + -7 = -7.211102551 Reorder the terms: -7 + x = -7.211102551 Solving -7 + x = -7.211102551 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 = -7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.211102551 + 7 x = -7.211102551 + 7 Combine like terms: -7.211102551 + 7 = -0.211102551 x = -0.211102551 Simplifying x = -0.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.211102551, -0.211102551}Solution
x = {14.211102551, -0.211102551}
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