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Simplifying 14x2 + -80x + 90 = 0 Reorder the terms: 90 + -80x + 14x2 = 0 Solving 90 + -80x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -40x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -40x + 7x2)' equal to zero and attempt to solve: Simplifying 45 + -40x + 7x2 = 0 Solving 45 + -40x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 6.428571429 + -5.714285714x + x2 = 0 Move the constant term to the right: Add '-6.428571429' to each side of the equation. 6.428571429 + -5.714285714x + -6.428571429 + x2 = 0 + -6.428571429 Reorder the terms: 6.428571429 + -6.428571429 + -5.714285714x + x2 = 0 + -6.428571429 Combine like terms: 6.428571429 + -6.428571429 = 0.000000000 0.000000000 + -5.714285714x + x2 = 0 + -6.428571429 -5.714285714x + x2 = 0 + -6.428571429 Combine like terms: 0 + -6.428571429 = -6.428571429 -5.714285714x + x2 = -6.428571429 The x term is -5.714285714x. Take half its coefficient (-2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. -5.714285714x + 8.163265305 + x2 = -6.428571429 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714x + x2 = -6.428571429 + 8.163265305 Combine like terms: -6.428571429 + 8.163265305 = 1.734693876 8.163265305 + -5.714285714x + x2 = 1.734693876 Factor a perfect square on the left side: (x + -2.857142857)(x + -2.857142857) = 1.734693876 Calculate the square root of the right side: 1.317077779 Break this problem into two subproblems by setting (x + -2.857142857) equal to 1.317077779 and -1.317077779.Subproblem 1
x + -2.857142857 = 1.317077779 Simplifying x + -2.857142857 = 1.317077779 Reorder the terms: -2.857142857 + x = 1.317077779 Solving -2.857142857 + x = 1.317077779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + x = 1.317077779 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + x = 1.317077779 + 2.857142857 x = 1.317077779 + 2.857142857 Combine like terms: 1.317077779 + 2.857142857 = 4.174220636 x = 4.174220636 Simplifying x = 4.174220636Subproblem 2
x + -2.857142857 = -1.317077779 Simplifying x + -2.857142857 = -1.317077779 Reorder the terms: -2.857142857 + x = -1.317077779 Solving -2.857142857 + x = -1.317077779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + x = -1.317077779 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + x = -1.317077779 + 2.857142857 x = -1.317077779 + 2.857142857 Combine like terms: -1.317077779 + 2.857142857 = 1.540065078 x = 1.540065078 Simplifying x = 1.540065078Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.174220636, 1.540065078}Solution
x = {4.174220636, 1.540065078}
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