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Simplifying 14x + 7 + 4 = 9x2 Reorder the terms: 7 + 4 + 14x = 9x2 Combine like terms: 7 + 4 = 11 11 + 14x = 9x2 Solving 11 + 14x = 9x2 Solving for variable 'x'. Combine like terms: 9x2 + -9x2 = 0 11 + 14x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.222222222 + -1.555555556x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + -1.555555556x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + -1.555555556x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + -1.555555556x + x2 = 0 + 1.222222222 -1.555555556x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 -1.555555556x + x2 = 1.222222222 The x term is -1.555555556x. Take half its coefficient (-0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. -1.555555556x + 0.6049382720 + x2 = 1.222222222 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = 1.222222222 + 0.6049382720 Combine like terms: 1.222222222 + 0.6049382720 = 1.827160494 0.6049382720 + -1.555555556x + x2 = 1.827160494 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 1.827160494 Calculate the square root of the right side: 1.351725007 Break this problem into two subproblems by setting (x + -0.777777778) equal to 1.351725007 and -1.351725007.Subproblem 1
x + -0.777777778 = 1.351725007 Simplifying x + -0.777777778 = 1.351725007 Reorder the terms: -0.777777778 + x = 1.351725007 Solving -0.777777778 + x = 1.351725007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = 1.351725007 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 1.351725007 + 0.777777778 x = 1.351725007 + 0.777777778 Combine like terms: 1.351725007 + 0.777777778 = 2.129502785 x = 2.129502785 Simplifying x = 2.129502785Subproblem 2
x + -0.777777778 = -1.351725007 Simplifying x + -0.777777778 = -1.351725007 Reorder the terms: -0.777777778 + x = -1.351725007 Solving -0.777777778 + x = -1.351725007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = -1.351725007 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -1.351725007 + 0.777777778 x = -1.351725007 + 0.777777778 Combine like terms: -1.351725007 + 0.777777778 = -0.573947229 x = -0.573947229 Simplifying x = -0.573947229Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.129502785, -0.573947229}
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