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Simplifying 9x2 + -42x + -49 = 0 Reorder the terms: -49 + -42x + 9x2 = 0 Solving -49 + -42x + 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'. -5.444444444 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '5.444444444' to each side of the equation. -5.444444444 + -4.666666667x + 5.444444444 + x2 = 0 + 5.444444444 Reorder the terms: -5.444444444 + 5.444444444 + -4.666666667x + x2 = 0 + 5.444444444 Combine like terms: -5.444444444 + 5.444444444 = 0.000000000 0.000000000 + -4.666666667x + x2 = 0 + 5.444444444 -4.666666667x + x2 = 0 + 5.444444444 Combine like terms: 0 + 5.444444444 = 5.444444444 -4.666666667x + x2 = 5.444444444 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 5.444444444 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 5.444444444 + 5.444444448 Combine like terms: 5.444444444 + 5.444444448 = 10.888888892 5.444444448 + -4.666666667x + x2 = 10.888888892 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 10.888888892 Calculate the square root of the right side: 3.299831646 Break this problem into two subproblems by setting (x + -2.333333334) equal to 3.299831646 and -3.299831646.Subproblem 1
x + -2.333333334 = 3.299831646 Simplifying x + -2.333333334 = 3.299831646 Reorder the terms: -2.333333334 + x = 3.299831646 Solving -2.333333334 + x = 3.299831646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 3.299831646 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 3.299831646 + 2.333333334 x = 3.299831646 + 2.333333334 Combine like terms: 3.299831646 + 2.333333334 = 5.63316498 x = 5.63316498 Simplifying x = 5.63316498Subproblem 2
x + -2.333333334 = -3.299831646 Simplifying x + -2.333333334 = -3.299831646 Reorder the terms: -2.333333334 + x = -3.299831646 Solving -2.333333334 + x = -3.299831646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -3.299831646 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -3.299831646 + 2.333333334 x = -3.299831646 + 2.333333334 Combine like terms: -3.299831646 + 2.333333334 = -0.966498312 x = -0.966498312 Simplifying x = -0.966498312Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.63316498, -0.966498312}
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