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Simplifying 2x2 + 4x + 12 = 7x2 + 14x + -75 Reorder the terms: 12 + 4x + 2x2 = 7x2 + 14x + -75 Reorder the terms: 12 + 4x + 2x2 = -75 + 14x + 7x2 Solving 12 + 4x + 2x2 = -75 + 14x + 7x2 Solving for variable 'x'. Reorder the terms: 12 + 75 + 4x + -14x + 2x2 + -7x2 = -75 + 14x + 7x2 + 75 + -14x + -7x2 Combine like terms: 12 + 75 = 87 87 + 4x + -14x + 2x2 + -7x2 = -75 + 14x + 7x2 + 75 + -14x + -7x2 Combine like terms: 4x + -14x = -10x 87 + -10x + 2x2 + -7x2 = -75 + 14x + 7x2 + 75 + -14x + -7x2 Combine like terms: 2x2 + -7x2 = -5x2 87 + -10x + -5x2 = -75 + 14x + 7x2 + 75 + -14x + -7x2 Reorder the terms: 87 + -10x + -5x2 = -75 + 75 + 14x + -14x + 7x2 + -7x2 Combine like terms: -75 + 75 = 0 87 + -10x + -5x2 = 0 + 14x + -14x + 7x2 + -7x2 87 + -10x + -5x2 = 14x + -14x + 7x2 + -7x2 Combine like terms: 14x + -14x = 0 87 + -10x + -5x2 = 0 + 7x2 + -7x2 87 + -10x + -5x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 87 + -10x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -17.4 + 2x + x2 = 0 Move the constant term to the right: Add '17.4' to each side of the equation. -17.4 + 2x + 17.4 + x2 = 0 + 17.4 Reorder the terms: -17.4 + 17.4 + 2x + x2 = 0 + 17.4 Combine like terms: -17.4 + 17.4 = 0.0 0.0 + 2x + x2 = 0 + 17.4 2x + x2 = 0 + 17.4 Combine like terms: 0 + 17.4 = 17.4 2x + x2 = 17.4 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 17.4 + 1 Reorder the terms: 1 + 2x + x2 = 17.4 + 1 Combine like terms: 17.4 + 1 = 18.4 1 + 2x + x2 = 18.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 18.4 Calculate the square root of the right side: 4.289522118 Break this problem into two subproblems by setting (x + 1) equal to 4.289522118 and -4.289522118.Subproblem 1
x + 1 = 4.289522118 Simplifying x + 1 = 4.289522118 Reorder the terms: 1 + x = 4.289522118 Solving 1 + x = 4.289522118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.289522118 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.289522118 + -1 x = 4.289522118 + -1 Combine like terms: 4.289522118 + -1 = 3.289522118 x = 3.289522118 Simplifying x = 3.289522118Subproblem 2
x + 1 = -4.289522118 Simplifying x + 1 = -4.289522118 Reorder the terms: 1 + x = -4.289522118 Solving 1 + x = -4.289522118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.289522118 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.289522118 + -1 x = -4.289522118 + -1 Combine like terms: -4.289522118 + -1 = -5.289522118 x = -5.289522118 Simplifying x = -5.289522118Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.289522118, -5.289522118}
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