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Simplifying 0 = 9x2 + 14x + -7 Reorder the terms: 0 = -7 + 14x + 9x2 Solving 0 = -7 + 14x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + -14x + -9x2 = -7 + 14x + 9x2 + 7 + -14x + -9x2 Reorder the terms: 7 + -14x + -9x2 = -7 + 7 + 14x + -14x + 9x2 + -9x2 Combine like terms: -7 + 7 = 0 7 + -14x + -9x2 = 0 + 14x + -14x + 9x2 + -9x2 7 + -14x + -9x2 = 14x + -14x + 9x2 + -9x2 Combine like terms: 14x + -14x = 0 7 + -14x + -9x2 = 0 + 9x2 + -9x2 7 + -14x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 7 + -14x + -9x2 = 0 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 = 0.398111694 x = 0.398111694 Simplifying x = 0.398111694Subproblem 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 = -1.95366725 x = -1.95366725 Simplifying x = -1.95366725Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.398111694, -1.95366725}
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