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Simplifying (2x + 7)(2x + -7) = 2 + 4(x + -5) * 2 Reorder the terms: (7 + 2x)(2x + -7) = 2 + 4(x + -5) * 2 Reorder the terms: (7 + 2x)(-7 + 2x) = 2 + 4(x + -5) * 2 Multiply (7 + 2x) * (-7 + 2x) (7(-7 + 2x) + 2x * (-7 + 2x)) = 2 + 4(x + -5) * 2 ((-7 * 7 + 2x * 7) + 2x * (-7 + 2x)) = 2 + 4(x + -5) * 2 ((-49 + 14x) + 2x * (-7 + 2x)) = 2 + 4(x + -5) * 2 (-49 + 14x + (-7 * 2x + 2x * 2x)) = 2 + 4(x + -5) * 2 (-49 + 14x + (-14x + 4x2)) = 2 + 4(x + -5) * 2 Combine like terms: 14x + -14x = 0 (-49 + 0 + 4x2) = 2 + 4(x + -5) * 2 (-49 + 4x2) = 2 + 4(x + -5) * 2 Reorder the terms: -49 + 4x2 = 2 + 4(-5 + x) * 2 Reorder the terms for easier multiplication: -49 + 4x2 = 2 + 4 * 2(-5 + x) Multiply 4 * 2 -49 + 4x2 = 2 + 8(-5 + x) -49 + 4x2 = 2 + (-5 * 8 + x * 8) -49 + 4x2 = 2 + (-40 + 8x) Combine like terms: 2 + -40 = -38 -49 + 4x2 = -38 + 8x Solving -49 + 4x2 = -38 + 8x Solving for variable 'x'. Reorder the terms: -49 + 38 + -8x + 4x2 = -38 + 8x + 38 + -8x Combine like terms: -49 + 38 = -11 -11 + -8x + 4x2 = -38 + 8x + 38 + -8x Reorder the terms: -11 + -8x + 4x2 = -38 + 38 + 8x + -8x Combine like terms: -38 + 38 = 0 -11 + -8x + 4x2 = 0 + 8x + -8x -11 + -8x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -11 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -2x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -2x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -2x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -2x + x2 = 0 + 2.75 -2x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -2x + x2 = 2.75 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 = 2.75 + 1 Reorder the terms: 1 + -2x + x2 = 2.75 + 1 Combine like terms: 2.75 + 1 = 3.75 1 + -2x + x2 = 3.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + -1) equal to 1.936491673 and -1.936491673.Subproblem 1
x + -1 = 1.936491673 Simplifying x + -1 = 1.936491673 Reorder the terms: -1 + x = 1.936491673 Solving -1 + x = 1.936491673 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 = 1.936491673 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.936491673 + 1 x = 1.936491673 + 1 Combine like terms: 1.936491673 + 1 = 2.936491673 x = 2.936491673 Simplifying x = 2.936491673Subproblem 2
x + -1 = -1.936491673 Simplifying x + -1 = -1.936491673 Reorder the terms: -1 + x = -1.936491673 Solving -1 + x = -1.936491673 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 = -1.936491673 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.936491673 + 1 x = -1.936491673 + 1 Combine like terms: -1.936491673 + 1 = -0.936491673 x = -0.936491673 Simplifying x = -0.936491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.936491673, -0.936491673}
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