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Simplifying 4x2 + -14x + -8 = 9 Reorder the terms: -8 + -14x + 4x2 = 9 Solving -8 + -14x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: -8 + -9 + -14x + 4x2 = 9 + -9 Combine like terms: -8 + -9 = -17 -17 + -14x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -17 + -14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -3.5x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -3.5x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -3.5x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -3.5x + x2 = 0 + 4.25 -3.5x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -3.5x + x2 = 4.25 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 = 4.25 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 4.25 + 3.0625 Combine like terms: 4.25 + 3.0625 = 7.3125 3.0625 + -3.5x + x2 = 7.3125 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 7.3125 Calculate the square root of the right side: 2.704163457 Break this problem into two subproblems by setting (x + -1.75) equal to 2.704163457 and -2.704163457.Subproblem 1
x + -1.75 = 2.704163457 Simplifying x + -1.75 = 2.704163457 Reorder the terms: -1.75 + x = 2.704163457 Solving -1.75 + x = 2.704163457 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 = 2.704163457 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.704163457 + 1.75 x = 2.704163457 + 1.75 Combine like terms: 2.704163457 + 1.75 = 4.454163457 x = 4.454163457 Simplifying x = 4.454163457Subproblem 2
x + -1.75 = -2.704163457 Simplifying x + -1.75 = -2.704163457 Reorder the terms: -1.75 + x = -2.704163457 Solving -1.75 + x = -2.704163457 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 = -2.704163457 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.704163457 + 1.75 x = -2.704163457 + 1.75 Combine like terms: -2.704163457 + 1.75 = -0.954163457 x = -0.954163457 Simplifying x = -0.954163457Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.454163457, -0.954163457}
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