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Simplifying 0.0000006192x4 + -1x2 + -72 = 0 Reorder the terms: -72 + -1x2 + 0.0000006192x4 = 0 Solving -72 + -1x2 + 0.0000006192x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0000006192 the coefficient of the squared term: Divide each side by '0.0000006192'. -116279069.8 + -1614987.08x2 + x4 = 0 Move the constant term to the right: Add '116279069.8' to each side of the equation. -116279069.8 + -1614987.08x2 + 116279069.8 + x4 = 0 + 116279069.8 Reorder the terms: -116279069.8 + 116279069.8 + -1614987.08x2 + x4 = 0 + 116279069.8 Combine like terms: -116279069.8 + 116279069.8 = 0.0 0.0 + -1614987.08x2 + x4 = 0 + 116279069.8 -1614987.08x2 + x4 = 0 + 116279069.8 Combine like terms: 0 + 116279069.8 = 116279069.8 -1614987.08x2 + x4 = 116279069.8 The x term is -1614987.08x2. Take half its coefficient (-807493.54). Square it (652045817100) and add it to both sides. Add '652045817100' to each side of the equation. -1614987.08x2 + 652045817100 + x4 = 116279069.8 + 652045817100 Reorder the terms: 652045817100 + -1614987.08x2 + x4 = 116279069.8 + 652045817100 Combine like terms: 116279069.8 + 652045817100 = 652162096169.8 652045817100 + -1614987.08x2 + x4 = 652162096169.8 Factor a perfect square on the left side: (x2 + -807493.54)(x2 + -807493.54) = 652162096169.8 Calculate the square root of the right side: 807565.53676454 Break this problem into two subproblems by setting (x2 + -807493.54) equal to 807565.53676454 and -807565.53676454.Subproblem 1
x2 + -807493.54 = 807565.53676454 Simplifying x2 + -807493.54 = 807565.53676454 Reorder the terms: -807493.54 + x2 = 807565.53676454 Solving -807493.54 + x2 = 807565.53676454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '807493.54' to each side of the equation. -807493.54 + 807493.54 + x2 = 807565.53676454 + 807493.54 Combine like terms: -807493.54 + 807493.54 = 0.00 0.00 + x2 = 807565.53676454 + 807493.54 x2 = 807565.53676454 + 807493.54 Combine like terms: 807565.53676454 + 807493.54 = 1615059.07676454 x2 = 1615059.07676454 Simplifying x2 = 1615059.07676454 Take the square root of each side: x = {-1270.849745943, 1270.849745943}Subproblem 2
x2 + -807493.54 = -807565.53676454 Simplifying x2 + -807493.54 = -807565.53676454 Reorder the terms: -807493.54 + x2 = -807565.53676454 Solving -807493.54 + x2 = -807565.53676454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '807493.54' to each side of the equation. -807493.54 + 807493.54 + x2 = -807565.53676454 + 807493.54 Combine like terms: -807493.54 + 807493.54 = 0.00 0.00 + x2 = -807565.53676454 + 807493.54 x2 = -807565.53676454 + 807493.54 Combine like terms: -807565.53676454 + 807493.54 = -71.99676454 x2 = -71.99676454 Simplifying x2 = -71.99676454 Reorder the terms: 71.99676454 + x2 = -71.99676454 + 71.99676454 Combine like terms: -71.99676454 + 71.99676454 = 0.00000000 71.99676454 + x2 = 0.00000000 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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