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Simplifying 28x2 + 16x + -8 = 0 Reorder the terms: -8 + 16x + 28x2 = 0 Solving -8 + 16x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 4x + 7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + 4x + 7x2)' equal to zero and attempt to solve: Simplifying -2 + 4x + 7x2 = 0 Solving -2 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.5714285714x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.5714285714x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + 0.2857142857 0.5714285714x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.5714285714x + x2 = 0.2857142857 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 0.2857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.2857142857 + 0.08163265305 Combine like terms: 0.2857142857 + 0.08163265305 = 0.36734693875 0.08163265305 + 0.5714285714x + x2 = 0.36734693875 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.36734693875 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.606091527 and -0.606091527.Subproblem 1
x + 0.2857142857 = 0.606091527 Simplifying x + 0.2857142857 = 0.606091527 Reorder the terms: 0.2857142857 + x = 0.606091527 Solving 0.2857142857 + x = 0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 0.606091527 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.606091527 + -0.2857142857 x = 0.606091527 + -0.2857142857 Combine like terms: 0.606091527 + -0.2857142857 = 0.3203772413 x = 0.3203772413 Simplifying x = 0.3203772413Subproblem 2
x + 0.2857142857 = -0.606091527 Simplifying x + 0.2857142857 = -0.606091527 Reorder the terms: 0.2857142857 + x = -0.606091527 Solving 0.2857142857 + x = -0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -0.606091527 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.606091527 + -0.2857142857 x = -0.606091527 + -0.2857142857 Combine like terms: -0.606091527 + -0.2857142857 = -0.8918058127 x = -0.8918058127 Simplifying x = -0.8918058127Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3203772413, -0.8918058127}Solution
x = {0.3203772413, -0.8918058127}
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