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Simplifying 2x(x + 3) + -7 = 7x Reorder the terms: 2x(3 + x) + -7 = 7x (3 * 2x + x * 2x) + -7 = 7x (6x + 2x2) + -7 = 7x Reorder the terms: -7 + 6x + 2x2 = 7x Solving -7 + 6x + 2x2 = 7x Solving for variable 'x'. Reorder the terms: -7 + 6x + -7x + 2x2 = 7x + -7x Combine like terms: 6x + -7x = -1x -7 + -1x + 2x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -7 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.5x + x2 = 0 + 3.5 -0.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.5x + x2 = 3.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 3.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 3.5 + 0.0625 Combine like terms: 3.5 + 0.0625 = 3.5625 0.0625 + -0.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + -0.25) equal to 1.887458609 and -1.887458609.Subproblem 1
x + -0.25 = 1.887458609 Simplifying x + -0.25 = 1.887458609 Reorder the terms: -0.25 + x = 1.887458609 Solving -0.25 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.887458609 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.887458609 + 0.25 x = 1.887458609 + 0.25 Combine like terms: 1.887458609 + 0.25 = 2.137458609 x = 2.137458609 Simplifying x = 2.137458609Subproblem 2
x + -0.25 = -1.887458609 Simplifying x + -0.25 = -1.887458609 Reorder the terms: -0.25 + x = -1.887458609 Solving -0.25 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.887458609 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.887458609 + 0.25 x = -1.887458609 + 0.25 Combine like terms: -1.887458609 + 0.25 = -1.637458609 x = -1.637458609 Simplifying x = -1.637458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.137458609, -1.637458609}
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