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Simplifying 8x3 + -28x2 + 14x = 0 Reorder the terms: 14x + -28x2 + 8x3 = 0 Solving 14x + -28x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(7 + -14x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + -14x + 4x2)' equal to zero and attempt to solve: Simplifying 7 + -14x + 4x2 = 0 Solving 7 + -14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -3.5x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -3.5x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -3.5x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -3.5x + x2 = 0 + -1.75 -3.5x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -3.5x + x2 = -1.75 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -1.75 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -1.75 + 3.0625 Combine like terms: -1.75 + 3.0625 = 1.3125 3.0625 + -3.5x + x2 = 1.3125 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + -1.75) equal to 1.145643924 and -1.145643924.Subproblem 1
x + -1.75 = 1.145643924 Simplifying x + -1.75 = 1.145643924 Reorder the terms: -1.75 + x = 1.145643924 Solving -1.75 + x = 1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.145643924 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.145643924 + 1.75 x = 1.145643924 + 1.75 Combine like terms: 1.145643924 + 1.75 = 2.895643924 x = 2.895643924 Simplifying x = 2.895643924Subproblem 2
x + -1.75 = -1.145643924 Simplifying x + -1.75 = -1.145643924 Reorder the terms: -1.75 + x = -1.145643924 Solving -1.75 + x = -1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.145643924 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.145643924 + 1.75 x = -1.145643924 + 1.75 Combine like terms: -1.145643924 + 1.75 = 0.604356076 x = 0.604356076 Simplifying x = 0.604356076Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.895643924, 0.604356076}Solution
x = {0, 2.895643924, 0.604356076}
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