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Simplifying x4 + 19x2 = 88 Reorder the terms: 19x2 + x4 = 88 Solving 19x2 + x4 = 88 Solving for variable 'x'. Reorder the terms: -88 + 19x2 + x4 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + 19x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 19x2 + 88 + x4 = 0 + 88 Reorder the terms: -88 + 88 + 19x2 + x4 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 19x2 + x4 = 0 + 88 19x2 + x4 = 0 + 88 Combine like terms: 0 + 88 = 88 19x2 + x4 = 88 The x term is 19x2. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x2 + 90.25 + x4 = 88 + 90.25 Reorder the terms: 90.25 + 19x2 + x4 = 88 + 90.25 Combine like terms: 88 + 90.25 = 178.25 90.25 + 19x2 + x4 = 178.25 Factor a perfect square on the left side: (x2 + 9.5)(x2 + 9.5) = 178.25 Calculate the square root of the right side: 13.351029923 Break this problem into two subproblems by setting (x2 + 9.5) equal to 13.351029923 and -13.351029923.Subproblem 1
x2 + 9.5 = 13.351029923 Simplifying x2 + 9.5 = 13.351029923 Reorder the terms: 9.5 + x2 = 13.351029923 Solving 9.5 + x2 = 13.351029923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x2 = 13.351029923 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x2 = 13.351029923 + -9.5 x2 = 13.351029923 + -9.5 Combine like terms: 13.351029923 + -9.5 = 3.851029923 x2 = 3.851029923 Simplifying x2 = 3.851029923 Take the square root of each side: x = {-1.962404118, 1.962404118}Subproblem 2
x2 + 9.5 = -13.351029923 Simplifying x2 + 9.5 = -13.351029923 Reorder the terms: 9.5 + x2 = -13.351029923 Solving 9.5 + x2 = -13.351029923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x2 = -13.351029923 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x2 = -13.351029923 + -9.5 x2 = -13.351029923 + -9.5 Combine like terms: -13.351029923 + -9.5 = -22.851029923 x2 = -22.851029923 Simplifying x2 = -22.851029923 Reorder the terms: 22.851029923 + x2 = -22.851029923 + 22.851029923 Combine like terms: -22.851029923 + 22.851029923 = 0.000000000 22.851029923 + 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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