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Simplifying -9x2 + 14x + 7 = 0 Reorder the terms: 7 + 14x + -9x2 = 0 Solving 7 + 14x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.7777777778 + -1.555555556x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -1.555555556x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -1.555555556x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -1.555555556x + x2 = 0 + 0.7777777778 -1.555555556x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -1.555555556x + x2 = 0.7777777778 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 = 0.7777777778 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = 0.7777777778 + 0.6049382720 Combine like terms: 0.7777777778 + 0.6049382720 = 1.3827160498 0.6049382720 + -1.555555556x + x2 = 1.3827160498 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 1.3827160498 Calculate the square root of the right side: 1.175889472 Break this problem into two subproblems by setting (x + -0.777777778) equal to 1.175889472 and -1.175889472.Subproblem 1
x + -0.777777778 = 1.175889472 Simplifying x + -0.777777778 = 1.175889472 Reorder the terms: -0.777777778 + x = 1.175889472 Solving -0.777777778 + x = 1.175889472 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 = 1.175889472 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 1.175889472 + 0.777777778 x = 1.175889472 + 0.777777778 Combine like terms: 1.175889472 + 0.777777778 = 1.95366725 x = 1.95366725 Simplifying x = 1.95366725Subproblem 2
x + -0.777777778 = -1.175889472 Simplifying x + -0.777777778 = -1.175889472 Reorder the terms: -0.777777778 + x = -1.175889472 Solving -0.777777778 + x = -1.175889472 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 = -1.175889472 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -1.175889472 + 0.777777778 x = -1.175889472 + 0.777777778 Combine like terms: -1.175889472 + 0.777777778 = -0.398111694 x = -0.398111694 Simplifying x = -0.398111694Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.95366725, -0.398111694}
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