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Simplifying x2 + -2x4 + -24x3 = 0 Reorder the terms: x2 + -24x3 + -2x4 = 0 Solving x2 + -24x3 + -2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(1 + -24x + -2x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(1 + -24x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + -24x + -2x2 = 0 Solving 1 + -24x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 12x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 12x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 12x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 12x + x2 = 0 + 0.5 12x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 12x + x2 = 0.5 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 0.5 + 36 Reorder the terms: 36 + 12x + x2 = 0.5 + 36 Combine like terms: 0.5 + 36 = 36.5 36 + 12x + x2 = 36.5 Factor a perfect square on the left side: (x + 6)(x + 6) = 36.5 Calculate the square root of the right side: 6.041522987 Break this problem into two subproblems by setting (x + 6) equal to 6.041522987 and -6.041522987.Subproblem 1
x + 6 = 6.041522987 Simplifying x + 6 = 6.041522987 Reorder the terms: 6 + x = 6.041522987 Solving 6 + x = 6.041522987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.041522987 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.041522987 + -6 x = 6.041522987 + -6 Combine like terms: 6.041522987 + -6 = 0.041522987 x = 0.041522987 Simplifying x = 0.041522987Subproblem 2
x + 6 = -6.041522987 Simplifying x + 6 = -6.041522987 Reorder the terms: 6 + x = -6.041522987 Solving 6 + x = -6.041522987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.041522987 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.041522987 + -6 x = -6.041522987 + -6 Combine like terms: -6.041522987 + -6 = -12.041522987 x = -12.041522987 Simplifying x = -12.041522987Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.041522987, -12.041522987}Solution
x = {0, 0.041522987, -12.041522987}
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