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Simplifying 7x(3x + 1) + -8(2x + 3) = 13 Reorder the terms: 7x(1 + 3x) + -8(2x + 3) = 13 (1 * 7x + 3x * 7x) + -8(2x + 3) = 13 (7x + 21x2) + -8(2x + 3) = 13 Reorder the terms: 7x + 21x2 + -8(3 + 2x) = 13 7x + 21x2 + (3 * -8 + 2x * -8) = 13 7x + 21x2 + (-24 + -16x) = 13 Reorder the terms: -24 + 7x + -16x + 21x2 = 13 Combine like terms: 7x + -16x = -9x -24 + -9x + 21x2 = 13 Solving -24 + -9x + 21x2 = 13 Solving for variable 'x'. Reorder the terms: -24 + -13 + -9x + 21x2 = 13 + -13 Combine like terms: -24 + -13 = -37 -37 + -9x + 21x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -37 + -9x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.761904762 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '1.761904762' to each side of the equation. -1.761904762 + -0.4285714286x + 1.761904762 + x2 = 0 + 1.761904762 Reorder the terms: -1.761904762 + 1.761904762 + -0.4285714286x + x2 = 0 + 1.761904762 Combine like terms: -1.761904762 + 1.761904762 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + 1.761904762 -0.4285714286x + x2 = 0 + 1.761904762 Combine like terms: 0 + 1.761904762 = 1.761904762 -0.4285714286x + x2 = 1.761904762 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 1.761904762 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 1.761904762 + 0.04591836735 Combine like terms: 1.761904762 + 0.04591836735 = 1.80782312935 0.04591836735 + -0.4285714286x + x2 = 1.80782312935 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 1.80782312935 Calculate the square root of the right side: 1.344553134 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 1.344553134 and -1.344553134.Subproblem 1
x + -0.2142857143 = 1.344553134 Simplifying x + -0.2142857143 = 1.344553134 Reorder the terms: -0.2142857143 + x = 1.344553134 Solving -0.2142857143 + x = 1.344553134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 1.344553134 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 1.344553134 + 0.2142857143 x = 1.344553134 + 0.2142857143 Combine like terms: 1.344553134 + 0.2142857143 = 1.5588388483 x = 1.5588388483 Simplifying x = 1.5588388483Subproblem 2
x + -0.2142857143 = -1.344553134 Simplifying x + -0.2142857143 = -1.344553134 Reorder the terms: -0.2142857143 + x = -1.344553134 Solving -0.2142857143 + x = -1.344553134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -1.344553134 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -1.344553134 + 0.2142857143 x = -1.344553134 + 0.2142857143 Combine like terms: -1.344553134 + 0.2142857143 = -1.1302674197 x = -1.1302674197 Simplifying x = -1.1302674197Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5588388483, -1.1302674197}
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