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Simplifying 10x4 + -19x2 + 7 = 0 Reorder the terms: 7 + -19x2 + 10x4 = 0 Solving 7 + -19x2 + 10x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -2x2)(7 + -5x2) = 0Subproblem 1
Set the factor '(1 + -2x2)' equal to zero and attempt to solve: Simplifying 1 + -2x2 = 0 Solving 1 + -2x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x2 = 0 + -1 -2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2x2 = -1 Divide each side by '-2'. x2 = 0.5 Simplifying x2 = 0.5 Take the square root of each side: x = {-0.707106781, 0.707106781}Subproblem 2
Set the factor '(7 + -5x2)' equal to zero and attempt to solve: Simplifying 7 + -5x2 = 0 Solving 7 + -5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x2 = 0 + -7 -5x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -5x2 = -7 Divide each side by '-5'. x2 = 1.4 Simplifying x2 = 1.4 Take the square root of each side: x = {-1.183215957, 1.183215957}Solution
x = {-0.707106781, 0.707106781, -1.183215957, 1.183215957}
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