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Simplifying 0 = 16x2 + 95x + 6 Reorder the terms: 0 = 6 + 95x + 16x2 Solving 0 = 6 + 95x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -95x + -16x2 = 6 + 95x + 16x2 + -6 + -95x + -16x2 Reorder the terms: -6 + -95x + -16x2 = 6 + -6 + 95x + -95x + 16x2 + -16x2 Combine like terms: 6 + -6 = 0 -6 + -95x + -16x2 = 0 + 95x + -95x + 16x2 + -16x2 -6 + -95x + -16x2 = 95x + -95x + 16x2 + -16x2 Combine like terms: 95x + -95x = 0 -6 + -95x + -16x2 = 0 + 16x2 + -16x2 -6 + -95x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -6 + -95x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 95x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 95x + 16x2)' equal to zero and attempt to solve: Simplifying 6 + 95x + 16x2 = 0 Solving 6 + 95x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.375 + 5.9375x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 5.9375x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 5.9375x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 5.9375x + x2 = 0 + -0.375 5.9375x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 5.9375x + x2 = -0.375 The x term is 5.9375x. Take half its coefficient (2.96875). Square it (8.813476563) and add it to both sides. Add '8.813476563' to each side of the equation. 5.9375x + 8.813476563 + x2 = -0.375 + 8.813476563 Reorder the terms: 8.813476563 + 5.9375x + x2 = -0.375 + 8.813476563 Combine like terms: -0.375 + 8.813476563 = 8.438476563 8.813476563 + 5.9375x + x2 = 8.438476563 Factor a perfect square on the left side: (x + 2.96875)(x + 2.96875) = 8.438476563 Calculate the square root of the right side: 2.904905603 Break this problem into two subproblems by setting (x + 2.96875) equal to 2.904905603 and -2.904905603.Subproblem 1
x + 2.96875 = 2.904905603 Simplifying x + 2.96875 = 2.904905603 Reorder the terms: 2.96875 + x = 2.904905603 Solving 2.96875 + x = 2.904905603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.96875' to each side of the equation. 2.96875 + -2.96875 + x = 2.904905603 + -2.96875 Combine like terms: 2.96875 + -2.96875 = 0.00000 0.00000 + x = 2.904905603 + -2.96875 x = 2.904905603 + -2.96875 Combine like terms: 2.904905603 + -2.96875 = -0.063844397 x = -0.063844397 Simplifying x = -0.063844397Subproblem 2
x + 2.96875 = -2.904905603 Simplifying x + 2.96875 = -2.904905603 Reorder the terms: 2.96875 + x = -2.904905603 Solving 2.96875 + x = -2.904905603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.96875' to each side of the equation. 2.96875 + -2.96875 + x = -2.904905603 + -2.96875 Combine like terms: 2.96875 + -2.96875 = 0.00000 0.00000 + x = -2.904905603 + -2.96875 x = -2.904905603 + -2.96875 Combine like terms: -2.904905603 + -2.96875 = -5.873655603 x = -5.873655603 Simplifying x = -5.873655603Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.063844397, -5.873655603}Solution
x = {-0.063844397, -5.873655603}
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