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Simplifying 90x9 + 63x8 + -48x7 = 0 Reorder the terms: -48x7 + 63x8 + 90x9 = 0 Solving -48x7 + 63x8 + 90x9 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x7'. 3x7(-16 + 21x + 30x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x7' equal to zero and attempt to solve: Simplifying x7 = 0 Solving x7 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x7 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-16 + 21x + 30x2)' equal to zero and attempt to solve: Simplifying -16 + 21x + 30x2 = 0 Solving -16 + 21x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.5333333333 + 0.7x + x2 = 0.0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + 0.7x + 0.5333333333 + x2 = 0.0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + 0.7x + x2 = 0.0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + 0.7x + x2 = 0.0 + 0.5333333333 0.7x + x2 = 0.0 + 0.5333333333 Combine like terms: 0.0 + 0.5333333333 = 0.5333333333 0.7x + x2 = 0.5333333333 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 = 0.5333333333 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 0.5333333333 + 0.1225 Combine like terms: 0.5333333333 + 0.1225 = 0.6558333333 0.1225 + 0.7x + x2 = 0.6558333333 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 0.6558333333 Calculate the square root of the right side: 0.809835374 Break this problem into two subproblems by setting (x + 0.35) equal to 0.809835374 and -0.809835374.Subproblem 1
x + 0.35 = 0.809835374 Simplifying x + 0.35 = 0.809835374 Reorder the terms: 0.35 + x = 0.809835374 Solving 0.35 + x = 0.809835374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.809835374 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.809835374 + -0.35 x = 0.809835374 + -0.35 Combine like terms: 0.809835374 + -0.35 = 0.459835374 x = 0.459835374 Simplifying x = 0.459835374Subproblem 2
x + 0.35 = -0.809835374 Simplifying x + 0.35 = -0.809835374 Reorder the terms: 0.35 + x = -0.809835374 Solving 0.35 + x = -0.809835374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.809835374 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.809835374 + -0.35 x = -0.809835374 + -0.35 Combine like terms: -0.809835374 + -0.35 = -1.159835374 x = -1.159835374 Simplifying x = -1.159835374Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.459835374, -1.159835374}Solution
x = {0.459835374, -1.159835374}
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