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Simplifying 25x10 + 28x9 + -14x8 = 0 Reorder the terms: -14x8 + 28x9 + 25x10 = 0 Solving -14x8 + 28x9 + 25x10 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x8'. x8(-14 + 28x + 25x2) = 0Subproblem 1
Set the factor 'x8' equal to zero and attempt to solve: Simplifying x8 = 0 Solving x8 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x8 = 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 '(-14 + 28x + 25x2)' equal to zero and attempt to solve: Simplifying -14 + 28x + 25x2 = 0 Solving -14 + 28x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.56 + 1.12x + x2 = 0 Move the constant term to the right: Add '0.56' to each side of the equation. -0.56 + 1.12x + 0.56 + x2 = 0 + 0.56 Reorder the terms: -0.56 + 0.56 + 1.12x + x2 = 0 + 0.56 Combine like terms: -0.56 + 0.56 = 0.00 0.00 + 1.12x + x2 = 0 + 0.56 1.12x + x2 = 0 + 0.56 Combine like terms: 0 + 0.56 = 0.56 1.12x + x2 = 0.56 The x term is 1.12x. Take half its coefficient (0.56). Square it (0.3136) and add it to both sides. Add '0.3136' to each side of the equation. 1.12x + 0.3136 + x2 = 0.56 + 0.3136 Reorder the terms: 0.3136 + 1.12x + x2 = 0.56 + 0.3136 Combine like terms: 0.56 + 0.3136 = 0.8736 0.3136 + 1.12x + x2 = 0.8736 Factor a perfect square on the left side: (x + 0.56)(x + 0.56) = 0.8736 Calculate the square root of the right side: 0.934665716 Break this problem into two subproblems by setting (x + 0.56) equal to 0.934665716 and -0.934665716.Subproblem 1
x + 0.56 = 0.934665716 Simplifying x + 0.56 = 0.934665716 Reorder the terms: 0.56 + x = 0.934665716 Solving 0.56 + x = 0.934665716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.56' to each side of the equation. 0.56 + -0.56 + x = 0.934665716 + -0.56 Combine like terms: 0.56 + -0.56 = 0.00 0.00 + x = 0.934665716 + -0.56 x = 0.934665716 + -0.56 Combine like terms: 0.934665716 + -0.56 = 0.374665716 x = 0.374665716 Simplifying x = 0.374665716Subproblem 2
x + 0.56 = -0.934665716 Simplifying x + 0.56 = -0.934665716 Reorder the terms: 0.56 + x = -0.934665716 Solving 0.56 + x = -0.934665716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.56' to each side of the equation. 0.56 + -0.56 + x = -0.934665716 + -0.56 Combine like terms: 0.56 + -0.56 = 0.00 0.00 + x = -0.934665716 + -0.56 x = -0.934665716 + -0.56 Combine like terms: -0.934665716 + -0.56 = -1.494665716 x = -1.494665716 Simplifying x = -1.494665716Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.374665716, -1.494665716}Solution
x = {0.374665716, -1.494665716}
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