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Simplifying 10x4 + -7x3 + 20x2 = 0 Reorder the terms: 20x2 + -7x3 + 10x4 = 0 Solving 20x2 + -7x3 + 10x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(20 + -7x + 10x2) = 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 '(20 + -7x + 10x2)' equal to zero and attempt to solve: Simplifying 20 + -7x + 10x2 = 0 Solving 20 + -7x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 2 + -0.7x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.7x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -0.7x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.7x + x2 = 0 + -2 -0.7x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.7x + x2 = -2 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = -2 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = -2 + 0.1225 Combine like terms: -2 + 0.1225 = -1.8775 0.1225 + -0.7x + x2 = -1.8775 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = -1.8775 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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