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Simplifying 5x4 + 30x3 + 10x2 = 4x2 + -1x2 Reorder the terms: 10x2 + 30x3 + 5x4 = 4x2 + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 10x2 + 30x3 + 5x4 = 3x2 Solving 10x2 + 30x3 + 5x4 = 3x2 Solving for variable 'x'. Reorder the terms: 10x2 + -3x2 + 30x3 + 5x4 = 3x2 + -3x2 Combine like terms: 10x2 + -3x2 = 7x2 7x2 + 30x3 + 5x4 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 7x2 + 30x3 + 5x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(7 + 30x + 5x2) = 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 '(7 + 30x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + 30x + 5x2 = 0 Solving 7 + 30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 6x + x2 = 0 + -1.4 6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 6x + x2 = -1.4 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -1.4 + 9 Reorder the terms: 9 + 6x + x2 = -1.4 + 9 Combine like terms: -1.4 + 9 = 7.6 9 + 6x + x2 = 7.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 7.6 Calculate the square root of the right side: 2.75680975 Break this problem into two subproblems by setting (x + 3) equal to 2.75680975 and -2.75680975.Subproblem 1
x + 3 = 2.75680975 Simplifying x + 3 = 2.75680975 Reorder the terms: 3 + x = 2.75680975 Solving 3 + x = 2.75680975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.75680975 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.75680975 + -3 x = 2.75680975 + -3 Combine like terms: 2.75680975 + -3 = -0.24319025 x = -0.24319025 Simplifying x = -0.24319025Subproblem 2
x + 3 = -2.75680975 Simplifying x + 3 = -2.75680975 Reorder the terms: 3 + x = -2.75680975 Solving 3 + x = -2.75680975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.75680975 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.75680975 + -3 x = -2.75680975 + -3 Combine like terms: -2.75680975 + -3 = -5.75680975 x = -5.75680975 Simplifying x = -5.75680975Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.24319025, -5.75680975}Solution
x = {0, -0.24319025, -5.75680975}
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