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Simplifying 8x4 + -9x2 = 18 Reorder the terms: -9x2 + 8x4 = 18 Solving -9x2 + 8x4 = 18 Solving for variable 'x'. Reorder the terms: -18 + -9x2 + 8x4 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -9x2 + 8x4 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.25 + -1.125x2 + x4 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1.125x2 + 2.25 + x4 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1.125x2 + x4 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1.125x2 + x4 = 0 + 2.25 -1.125x2 + x4 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1.125x2 + x4 = 2.25 The x term is -1.125x2. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x2 + 0.31640625 + x4 = 2.25 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x2 + x4 = 2.25 + 0.31640625 Combine like terms: 2.25 + 0.31640625 = 2.56640625 0.31640625 + -1.125x2 + x4 = 2.56640625 Factor a perfect square on the left side: (x2 + -0.5625)(x2 + -0.5625) = 2.56640625 Calculate the square root of the right side: 1.602000702 Break this problem into two subproblems by setting (x2 + -0.5625) equal to 1.602000702 and -1.602000702.Subproblem 1
x2 + -0.5625 = 1.602000702 Simplifying x2 + -0.5625 = 1.602000702 Reorder the terms: -0.5625 + x2 = 1.602000702 Solving -0.5625 + x2 = 1.602000702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x2 = 1.602000702 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x2 = 1.602000702 + 0.5625 x2 = 1.602000702 + 0.5625 Combine like terms: 1.602000702 + 0.5625 = 2.164500702 x2 = 2.164500702 Simplifying x2 = 2.164500702 Take the square root of each side: x = {-1.471224219, 1.471224219}Subproblem 2
x2 + -0.5625 = -1.602000702 Simplifying x2 + -0.5625 = -1.602000702 Reorder the terms: -0.5625 + x2 = -1.602000702 Solving -0.5625 + x2 = -1.602000702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x2 = -1.602000702 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x2 = -1.602000702 + 0.5625 x2 = -1.602000702 + 0.5625 Combine like terms: -1.602000702 + 0.5625 = -1.039500702 x2 = -1.039500702 Simplifying x2 = -1.039500702 Reorder the terms: 1.039500702 + x2 = -1.039500702 + 1.039500702 Combine like terms: -1.039500702 + 1.039500702 = 0.000000000 1.039500702 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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