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Simplifying (7x2 + -3x + 13) + (9x2 + 9x + -67) = 0 Reorder the terms: (13 + -3x + 7x2) + (9x2 + 9x + -67) = 0 Remove parenthesis around (13 + -3x + 7x2) 13 + -3x + 7x2 + (9x2 + 9x + -67) = 0 Reorder the terms: 13 + -3x + 7x2 + (-67 + 9x + 9x2) = 0 Remove parenthesis around (-67 + 9x + 9x2) 13 + -3x + 7x2 + -67 + 9x + 9x2 = 0 Reorder the terms: 13 + -67 + -3x + 9x + 7x2 + 9x2 = 0 Combine like terms: 13 + -67 = -54 -54 + -3x + 9x + 7x2 + 9x2 = 0 Combine like terms: -3x + 9x = 6x -54 + 6x + 7x2 + 9x2 = 0 Combine like terms: 7x2 + 9x2 = 16x2 -54 + 6x + 16x2 = 0 Solving -54 + 6x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 3x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + 3x + 8x2)' equal to zero and attempt to solve: Simplifying -27 + 3x + 8x2 = 0 Solving -27 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.375 + 0.375x + x2 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + 0.375x + 3.375 + x2 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + 0.375x + x2 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + 0.375x + x2 = 0 + 3.375 0.375x + x2 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 0.375x + x2 = 3.375 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 3.375 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 3.375 + 0.03515625 Combine like terms: 3.375 + 0.03515625 = 3.41015625 0.03515625 + 0.375x + x2 = 3.41015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 3.41015625 Calculate the square root of the right side: 1.846660838 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.846660838 and -1.846660838.Subproblem 1
x + 0.1875 = 1.846660838 Simplifying x + 0.1875 = 1.846660838 Reorder the terms: 0.1875 + x = 1.846660838 Solving 0.1875 + x = 1.846660838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.846660838 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.846660838 + -0.1875 x = 1.846660838 + -0.1875 Combine like terms: 1.846660838 + -0.1875 = 1.659160838 x = 1.659160838 Simplifying x = 1.659160838Subproblem 2
x + 0.1875 = -1.846660838 Simplifying x + 0.1875 = -1.846660838 Reorder the terms: 0.1875 + x = -1.846660838 Solving 0.1875 + x = -1.846660838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.846660838 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.846660838 + -0.1875 x = -1.846660838 + -0.1875 Combine like terms: -1.846660838 + -0.1875 = -2.034160838 x = -2.034160838 Simplifying x = -2.034160838Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.659160838, -2.034160838}Solution
x = {1.659160838, -2.034160838}
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