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Simplifying 9x2 + -42x + 49 = 10 Reorder the terms: 49 + -42x + 9x2 = 10 Solving 49 + -42x + 9x2 = 10 Solving for variable 'x'. Reorder the terms: 49 + -10 + -42x + 9x2 = 10 + -10 Combine like terms: 49 + -10 = 39 39 + -42x + 9x2 = 10 + -10 Combine like terms: 10 + -10 = 0 39 + -42x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(13 + -14x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(13 + -14x + 3x2)' equal to zero and attempt to solve: Simplifying 13 + -14x + 3x2 = 0 Solving 13 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.333333333 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + -4.666666667x + -4.333333333 + x2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + -4.666666667x + x2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + -4.666666667x + x2 = 0 + -4.333333333 -4.666666667x + x2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 -4.666666667x + x2 = -4.333333333 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 = -4.333333333 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = -4.333333333 + 5.444444448 Combine like terms: -4.333333333 + 5.444444448 = 1.111111115 5.444444448 + -4.666666667x + x2 = 1.111111115 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 1.111111115 Calculate the square root of the right side: 1.054092555 Break this problem into two subproblems by setting (x + -2.333333334) equal to 1.054092555 and -1.054092555.Subproblem 1
x + -2.333333334 = 1.054092555 Simplifying x + -2.333333334 = 1.054092555 Reorder the terms: -2.333333334 + x = 1.054092555 Solving -2.333333334 + x = 1.054092555 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 = 1.054092555 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 1.054092555 + 2.333333334 x = 1.054092555 + 2.333333334 Combine like terms: 1.054092555 + 2.333333334 = 3.387425889 x = 3.387425889 Simplifying x = 3.387425889Subproblem 2
x + -2.333333334 = -1.054092555 Simplifying x + -2.333333334 = -1.054092555 Reorder the terms: -2.333333334 + x = -1.054092555 Solving -2.333333334 + x = -1.054092555 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 = -1.054092555 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -1.054092555 + 2.333333334 x = -1.054092555 + 2.333333334 Combine like terms: -1.054092555 + 2.333333334 = 1.279240779 x = 1.279240779 Simplifying x = 1.279240779Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.387425889, 1.279240779}Solution
x = {3.387425889, 1.279240779}
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