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Simplifying 14x2 + 52x + -38 = 0 Reorder the terms: -38 + 52x + 14x2 = 0 Solving -38 + 52x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + 26x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 26x + 7x2)' equal to zero and attempt to solve: Simplifying -19 + 26x + 7x2 = 0 Solving -19 + 26x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.714285714 + 3.714285714x + x2 = 0 Move the constant term to the right: Add '2.714285714' to each side of the equation. -2.714285714 + 3.714285714x + 2.714285714 + x2 = 0 + 2.714285714 Reorder the terms: -2.714285714 + 2.714285714 + 3.714285714x + x2 = 0 + 2.714285714 Combine like terms: -2.714285714 + 2.714285714 = 0.000000000 0.000000000 + 3.714285714x + x2 = 0 + 2.714285714 3.714285714x + x2 = 0 + 2.714285714 Combine like terms: 0 + 2.714285714 = 2.714285714 3.714285714x + x2 = 2.714285714 The x term is 3.714285714x. Take half its coefficient (1.857142857). Square it (3.448979591) and add it to both sides. Add '3.448979591' to each side of the equation. 3.714285714x + 3.448979591 + x2 = 2.714285714 + 3.448979591 Reorder the terms: 3.448979591 + 3.714285714x + x2 = 2.714285714 + 3.448979591 Combine like terms: 2.714285714 + 3.448979591 = 6.163265305 3.448979591 + 3.714285714x + x2 = 6.163265305 Factor a perfect square on the left side: (x + 1.857142857)(x + 1.857142857) = 6.163265305 Calculate the square root of the right side: 2.482592456 Break this problem into two subproblems by setting (x + 1.857142857) equal to 2.482592456 and -2.482592456.Subproblem 1
x + 1.857142857 = 2.482592456 Simplifying x + 1.857142857 = 2.482592456 Reorder the terms: 1.857142857 + x = 2.482592456 Solving 1.857142857 + x = 2.482592456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + x = 2.482592456 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + x = 2.482592456 + -1.857142857 x = 2.482592456 + -1.857142857 Combine like terms: 2.482592456 + -1.857142857 = 0.625449599 x = 0.625449599 Simplifying x = 0.625449599Subproblem 2
x + 1.857142857 = -2.482592456 Simplifying x + 1.857142857 = -2.482592456 Reorder the terms: 1.857142857 + x = -2.482592456 Solving 1.857142857 + x = -2.482592456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + x = -2.482592456 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + x = -2.482592456 + -1.857142857 x = -2.482592456 + -1.857142857 Combine like terms: -2.482592456 + -1.857142857 = -4.339735313 x = -4.339735313 Simplifying x = -4.339735313Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.625449599, -4.339735313}Solution
x = {0.625449599, -4.339735313}
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