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Simplifying 0 = 9x2 + -14x + 4 Reorder the terms: 0 = 4 + -14x + 9x2 Solving 0 = 4 + -14x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + 14x + -9x2 = 4 + -14x + 9x2 + -4 + 14x + -9x2 Reorder the terms: -4 + 14x + -9x2 = 4 + -4 + -14x + 14x + 9x2 + -9x2 Combine like terms: 4 + -4 = 0 -4 + 14x + -9x2 = 0 + -14x + 14x + 9x2 + -9x2 -4 + 14x + -9x2 = -14x + 14x + 9x2 + -9x2 Combine like terms: -14x + 14x = 0 -4 + 14x + -9x2 = 0 + 9x2 + -9x2 -4 + 14x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -4 + 14x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.4444444444 + -1.555555556x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -1.555555556x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -1.555555556x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -1.555555556x + x2 = 0 + -0.4444444444 -1.555555556x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -1.555555556x + x2 = -0.4444444444 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 = -0.4444444444 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = -0.4444444444 + 0.6049382720 Combine like terms: -0.4444444444 + 0.6049382720 = 0.1604938276 0.6049382720 + -1.555555556x + x2 = 0.1604938276 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 0.1604938276 Calculate the square root of the right side: 0.400616809 Break this problem into two subproblems by setting (x + -0.777777778) equal to 0.400616809 and -0.400616809.Subproblem 1
x + -0.777777778 = 0.400616809 Simplifying x + -0.777777778 = 0.400616809 Reorder the terms: -0.777777778 + x = 0.400616809 Solving -0.777777778 + x = 0.400616809 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 = 0.400616809 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 0.400616809 + 0.777777778 x = 0.400616809 + 0.777777778 Combine like terms: 0.400616809 + 0.777777778 = 1.178394587 x = 1.178394587 Simplifying x = 1.178394587Subproblem 2
x + -0.777777778 = -0.400616809 Simplifying x + -0.777777778 = -0.400616809 Reorder the terms: -0.777777778 + x = -0.400616809 Solving -0.777777778 + x = -0.400616809 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 = -0.400616809 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -0.400616809 + 0.777777778 x = -0.400616809 + 0.777777778 Combine like terms: -0.400616809 + 0.777777778 = 0.377160969 x = 0.377160969 Simplifying x = 0.377160969Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.178394587, 0.377160969}
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