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Simplifying 9x2 + 25 = 42x Reorder the terms: 25 + 9x2 = 42x Solving 25 + 9x2 = 42x Solving for variable 'x'. Reorder the terms: 25 + -42x + 9x2 = 42x + -42x Combine like terms: 42x + -42x = 0 25 + -42x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.777777778 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '-2.777777778' to each side of the equation. 2.777777778 + -4.666666667x + -2.777777778 + x2 = 0 + -2.777777778 Reorder the terms: 2.777777778 + -2.777777778 + -4.666666667x + x2 = 0 + -2.777777778 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 0.000000000 + -4.666666667x + x2 = 0 + -2.777777778 -4.666666667x + x2 = 0 + -2.777777778 Combine like terms: 0 + -2.777777778 = -2.777777778 -4.666666667x + x2 = -2.777777778 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 = -2.777777778 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = -2.777777778 + 5.444444448 Combine like terms: -2.777777778 + 5.444444448 = 2.66666667 5.444444448 + -4.666666667x + x2 = 2.66666667 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 2.66666667 Calculate the square root of the right side: 1.632993163 Break this problem into two subproblems by setting (x + -2.333333334) equal to 1.632993163 and -1.632993163.Subproblem 1
x + -2.333333334 = 1.632993163 Simplifying x + -2.333333334 = 1.632993163 Reorder the terms: -2.333333334 + x = 1.632993163 Solving -2.333333334 + x = 1.632993163 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 = 1.632993163 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 1.632993163 + 2.333333334 x = 1.632993163 + 2.333333334 Combine like terms: 1.632993163 + 2.333333334 = 3.966326497 x = 3.966326497 Simplifying x = 3.966326497Subproblem 2
x + -2.333333334 = -1.632993163 Simplifying x + -2.333333334 = -1.632993163 Reorder the terms: -2.333333334 + x = -1.632993163 Solving -2.333333334 + x = -1.632993163 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 = -1.632993163 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -1.632993163 + 2.333333334 x = -1.632993163 + 2.333333334 Combine like terms: -1.632993163 + 2.333333334 = 0.700340171 x = 0.700340171 Simplifying x = 0.700340171Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.966326497, 0.700340171}
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