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Simplifying 10x4 + 3x2 + -12 = 0 Reorder the terms: -12 + 3x2 + 10x4 = 0 Solving -12 + 3x2 + 10x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.2 + 0.3x2 + x4 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.3x2 + 1.2 + x4 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.3x2 + x4 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.3x2 + x4 = 0 + 1.2 0.3x2 + x4 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.3x2 + x4 = 1.2 The x term is 0.3x2. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x2 + 0.0225 + x4 = 1.2 + 0.0225 Reorder the terms: 0.0225 + 0.3x2 + x4 = 1.2 + 0.0225 Combine like terms: 1.2 + 0.0225 = 1.2225 0.0225 + 0.3x2 + x4 = 1.2225 Factor a perfect square on the left side: (x2 + 0.15)(x2 + 0.15) = 1.2225 Calculate the square root of the right side: 1.105667219 Break this problem into two subproblems by setting (x2 + 0.15) equal to 1.105667219 and -1.105667219.Subproblem 1
x2 + 0.15 = 1.105667219 Simplifying x2 + 0.15 = 1.105667219 Reorder the terms: 0.15 + x2 = 1.105667219 Solving 0.15 + x2 = 1.105667219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x2 = 1.105667219 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x2 = 1.105667219 + -0.15 x2 = 1.105667219 + -0.15 Combine like terms: 1.105667219 + -0.15 = 0.955667219 x2 = 0.955667219 Simplifying x2 = 0.955667219 Take the square root of each side: x = {-0.977582334, 0.977582334}Subproblem 2
x2 + 0.15 = -1.105667219 Simplifying x2 + 0.15 = -1.105667219 Reorder the terms: 0.15 + x2 = -1.105667219 Solving 0.15 + x2 = -1.105667219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x2 = -1.105667219 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x2 = -1.105667219 + -0.15 x2 = -1.105667219 + -0.15 Combine like terms: -1.105667219 + -0.15 = -1.255667219 x2 = -1.255667219 Simplifying x2 = -1.255667219 Reorder the terms: 1.255667219 + x2 = -1.255667219 + 1.255667219 Combine like terms: -1.255667219 + 1.255667219 = 0.000000000 1.255667219 + 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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