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Simplifying 9x2 + 42x + 16 = 0 Reorder the terms: 16 + 42x + 9x2 = 0 Solving 16 + 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'. 1.777777778 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + 4.666666667x + -1.777777778 + x2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + 4.666666667x + x2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + 4.666666667x + x2 = 0 + -1.777777778 4.666666667x + x2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 4.666666667x + x2 = -1.777777778 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 = -1.777777778 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = -1.777777778 + 5.444444448 Combine like terms: -1.777777778 + 5.444444448 = 3.66666667 5.444444448 + 4.666666667x + x2 = 3.66666667 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 3.66666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (x + 2.333333334) equal to 1.914854216 and -1.914854216.Subproblem 1
x + 2.333333334 = 1.914854216 Simplifying x + 2.333333334 = 1.914854216 Reorder the terms: 2.333333334 + x = 1.914854216 Solving 2.333333334 + x = 1.914854216 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 = 1.914854216 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 1.914854216 + -2.333333334 x = 1.914854216 + -2.333333334 Combine like terms: 1.914854216 + -2.333333334 = -0.418479118 x = -0.418479118 Simplifying x = -0.418479118Subproblem 2
x + 2.333333334 = -1.914854216 Simplifying x + 2.333333334 = -1.914854216 Reorder the terms: 2.333333334 + x = -1.914854216 Solving 2.333333334 + x = -1.914854216 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 = -1.914854216 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -1.914854216 + -2.333333334 x = -1.914854216 + -2.333333334 Combine like terms: -1.914854216 + -2.333333334 = -4.24818755 x = -4.24818755 Simplifying x = -4.24818755Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.418479118, -4.24818755}
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