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Simplifying 15x4 + -120x2 + 70 = 0 Reorder the terms: 70 + -120x2 + 15x4 = 0 Solving 70 + -120x2 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(14 + -24x2 + 3x4) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(14 + -24x2 + 3x4)' equal to zero and attempt to solve: Simplifying 14 + -24x2 + 3x4 = 0 Solving 14 + -24x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.666666667 + -8x2 + x4 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + -8x2 + -4.666666667 + x4 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + -8x2 + x4 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + -8x2 + x4 = 0 + -4.666666667 -8x2 + x4 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 -8x2 + x4 = -4.666666667 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -4.666666667 + 16 Reorder the terms: 16 + -8x2 + x4 = -4.666666667 + 16 Combine like terms: -4.666666667 + 16 = 11.333333333 16 + -8x2 + x4 = 11.333333333 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 11.333333333 Calculate the square root of the right side: 3.366501646 Break this problem into two subproblems by setting (x2 + -4) equal to 3.366501646 and -3.366501646.Subproblem 1
x2 + -4 = 3.366501646 Simplifying x2 + -4 = 3.366501646 Reorder the terms: -4 + x2 = 3.366501646 Solving -4 + x2 = 3.366501646 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 + x2 = 3.366501646 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.366501646 + 4 x2 = 3.366501646 + 4 Combine like terms: 3.366501646 + 4 = 7.366501646 x2 = 7.366501646 Simplifying x2 = 7.366501646 Take the square root of each side: x = {-2.714129998, 2.714129998}Subproblem 2
x2 + -4 = -3.366501646 Simplifying x2 + -4 = -3.366501646 Reorder the terms: -4 + x2 = -3.366501646 Solving -4 + x2 = -3.366501646 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 + x2 = -3.366501646 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.366501646 + 4 x2 = -3.366501646 + 4 Combine like terms: -3.366501646 + 4 = 0.633498354 x2 = 0.633498354 Simplifying x2 = 0.633498354 Take the square root of each side: x = {-0.795926098, 0.795926098}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.714129998, 2.714129998, -0.795926098, 0.795926098}Solution
x = {-2.714129998, 2.714129998, -0.795926098, 0.795926098}
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