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Simplifying 4x(x + 5) + -11 = 4(4x) + 17x + 7 Reorder the terms: 4x(5 + x) + -11 = 4(4x) + 17x + 7 (5 * 4x + x * 4x) + -11 = 4(4x) + 17x + 7 (20x + 4x2) + -11 = 4(4x) + 17x + 7 Reorder the terms: -11 + 20x + 4x2 = 4(4x) + 17x + 7 Remove parenthesis around (4x) -11 + 20x + 4x2 = 4 * 4x + 17x + 7 Multiply 4 * 4 -11 + 20x + 4x2 = 16x + 17x + 7 Reorder the terms: -11 + 20x + 4x2 = 7 + 16x + 17x Combine like terms: 16x + 17x = 33x -11 + 20x + 4x2 = 7 + 33x Solving -11 + 20x + 4x2 = 7 + 33x Solving for variable 'x'. Reorder the terms: -11 + -7 + 20x + -33x + 4x2 = 7 + 33x + -7 + -33x Combine like terms: -11 + -7 = -18 -18 + 20x + -33x + 4x2 = 7 + 33x + -7 + -33x Combine like terms: 20x + -33x = -13x -18 + -13x + 4x2 = 7 + 33x + -7 + -33x Reorder the terms: -18 + -13x + 4x2 = 7 + -7 + 33x + -33x Combine like terms: 7 + -7 = 0 -18 + -13x + 4x2 = 0 + 33x + -33x -18 + -13x + 4x2 = 33x + -33x Combine like terms: 33x + -33x = 0 -18 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + -3.25x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -3.25x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -3.25x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -3.25x + x2 = 0 + 4.5 -3.25x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -3.25x + x2 = 4.5 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 4.5 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 4.5 + 2.640625 Combine like terms: 4.5 + 2.640625 = 7.140625 2.640625 + -3.25x + x2 = 7.140625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 7.140625 Calculate the square root of the right side: 2.672194791 Break this problem into two subproblems by setting (x + -1.625) equal to 2.672194791 and -2.672194791.Subproblem 1
x + -1.625 = 2.672194791 Simplifying x + -1.625 = 2.672194791 Reorder the terms: -1.625 + x = 2.672194791 Solving -1.625 + x = 2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 2.672194791 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 2.672194791 + 1.625 x = 2.672194791 + 1.625 Combine like terms: 2.672194791 + 1.625 = 4.297194791 x = 4.297194791 Simplifying x = 4.297194791Subproblem 2
x + -1.625 = -2.672194791 Simplifying x + -1.625 = -2.672194791 Reorder the terms: -1.625 + x = -2.672194791 Solving -1.625 + x = -2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -2.672194791 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -2.672194791 + 1.625 x = -2.672194791 + 1.625 Combine like terms: -2.672194791 + 1.625 = -1.047194791 x = -1.047194791 Simplifying x = -1.047194791Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.297194791, -1.047194791}
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