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Simplifying -2x4 + 16x3 + 14x2 = 0 Reorder the terms: 14x2 + 16x3 + -2x4 = 0 Solving 14x2 + 16x3 + -2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(7 + 8x + -1x2) = 0 Ignore the factor 2.Subproblem 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 '(7 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying 7 + 8x + -1x2 = 0 Solving 7 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -8x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -8x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -8x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8x + x2 = 0 + 7 -8x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -8x + x2 = 7 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 7 + 16 Reorder the terms: 16 + -8x + x2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + -8x + x2 = 23 Factor a perfect square on the left side: (x + -4)(x + -4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + -4) equal to 4.795831523 and -4.795831523.Subproblem 1
x + -4 = 4.795831523 Simplifying x + -4 = 4.795831523 Reorder the terms: -4 + x = 4.795831523 Solving -4 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.795831523 + 4 x = 4.795831523 + 4 Combine like terms: 4.795831523 + 4 = 8.795831523 x = 8.795831523 Simplifying x = 8.795831523Subproblem 2
x + -4 = -4.795831523 Simplifying x + -4 = -4.795831523 Reorder the terms: -4 + x = -4.795831523 Solving -4 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.795831523 + 4 x = -4.795831523 + 4 Combine like terms: -4.795831523 + 4 = -0.795831523 x = -0.795831523 Simplifying x = -0.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.795831523, -0.795831523}Solution
x = {0, 8.795831523, -0.795831523}
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