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Simplifying 6x + 7 = 4x2 + -14 Reorder the terms: 7 + 6x = 4x2 + -14 Reorder the terms: 7 + 6x = -14 + 4x2 Solving 7 + 6x = -14 + 4x2 Solving for variable 'x'. Reorder the terms: 7 + 14 + 6x + -4x2 = -14 + 4x2 + 14 + -4x2 Combine like terms: 7 + 14 = 21 21 + 6x + -4x2 = -14 + 4x2 + 14 + -4x2 Reorder the terms: 21 + 6x + -4x2 = -14 + 14 + 4x2 + -4x2 Combine like terms: -14 + 14 = 0 21 + 6x + -4x2 = 0 + 4x2 + -4x2 21 + 6x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 21 + 6x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.25 + -1.5x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -1.5x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -1.5x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -1.5x + x2 = 0 + 5.25 -1.5x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -1.5x + x2 = 5.25 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 5.25 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 5.25 + 0.5625 Combine like terms: 5.25 + 0.5625 = 5.8125 0.5625 + -1.5x + x2 = 5.8125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 5.8125 Calculate the square root of the right side: 2.41091269 Break this problem into two subproblems by setting (x + -0.75) equal to 2.41091269 and -2.41091269.Subproblem 1
x + -0.75 = 2.41091269 Simplifying x + -0.75 = 2.41091269 Reorder the terms: -0.75 + x = 2.41091269 Solving -0.75 + x = 2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.41091269 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.41091269 + 0.75 x = 2.41091269 + 0.75 Combine like terms: 2.41091269 + 0.75 = 3.16091269 x = 3.16091269 Simplifying x = 3.16091269Subproblem 2
x + -0.75 = -2.41091269 Simplifying x + -0.75 = -2.41091269 Reorder the terms: -0.75 + x = -2.41091269 Solving -0.75 + x = -2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.41091269 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.41091269 + 0.75 x = -2.41091269 + 0.75 Combine like terms: -2.41091269 + 0.75 = -1.66091269 x = -1.66091269 Simplifying x = -1.66091269Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.16091269, -1.66091269}
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