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Simplifying 1107x2 + 1476x + 12 = 0 Reorder the terms: 12 + 1476x + 1107x2 = 0 Solving 12 + 1476x + 1107x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 492x + 369x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 492x + 369x2)' equal to zero and attempt to solve: Simplifying 4 + 492x + 369x2 = 0 Solving 4 + 492x + 369x2 = 0 Begin completing the square. Divide all terms by 369 the coefficient of the squared term: Divide each side by '369'. 0.0108401084 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.0108401084' to each side of the equation. 0.0108401084 + 1.333333333x + -0.0108401084 + x2 = 0 + -0.0108401084 Reorder the terms: 0.0108401084 + -0.0108401084 + 1.333333333x + x2 = 0 + -0.0108401084 Combine like terms: 0.0108401084 + -0.0108401084 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + -0.0108401084 1.333333333x + x2 = 0 + -0.0108401084 Combine like terms: 0 + -0.0108401084 = -0.0108401084 1.333333333x + x2 = -0.0108401084 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -0.0108401084 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.0108401084 + 0.4444444442 Combine like terms: -0.0108401084 + 0.4444444442 = 0.4336043358 0.4444444442 + 1.333333333x + x2 = 0.4336043358 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.4336043358 Calculate the square root of the right side: 0.658486398 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.658486398 and -0.658486398.Subproblem 1
x + 0.6666666665 = 0.658486398 Simplifying x + 0.6666666665 = 0.658486398 Reorder the terms: 0.6666666665 + x = 0.658486398 Solving 0.6666666665 + x = 0.658486398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 0.658486398 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.658486398 + -0.6666666665 x = 0.658486398 + -0.6666666665 Combine like terms: 0.658486398 + -0.6666666665 = -0.0081802685 x = -0.0081802685 Simplifying x = -0.0081802685Subproblem 2
x + 0.6666666665 = -0.658486398 Simplifying x + 0.6666666665 = -0.658486398 Reorder the terms: 0.6666666665 + x = -0.658486398 Solving 0.6666666665 + x = -0.658486398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -0.658486398 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.658486398 + -0.6666666665 x = -0.658486398 + -0.6666666665 Combine like terms: -0.658486398 + -0.6666666665 = -1.3251530645 x = -1.3251530645 Simplifying x = -1.3251530645Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0081802685, -1.3251530645}Solution
x = {-0.0081802685, -1.3251530645}
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