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Simplifying 5x(7x + -3) = 2 + 5x Reorder the terms: 5x(-3 + 7x) = 2 + 5x (-3 * 5x + 7x * 5x) = 2 + 5x (-15x + 35x2) = 2 + 5x Solving -15x + 35x2 = 2 + 5x Solving for variable 'x'. Reorder the terms: -2 + -15x + -5x + 35x2 = 2 + 5x + -2 + -5x Combine like terms: -15x + -5x = -20x -2 + -20x + 35x2 = 2 + 5x + -2 + -5x Reorder the terms: -2 + -20x + 35x2 = 2 + -2 + 5x + -5x Combine like terms: 2 + -2 = 0 -2 + -20x + 35x2 = 0 + 5x + -5x -2 + -20x + 35x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -2 + -20x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.05714285714 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + -0.5714285714x + 0.05714285714 + x2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + -0.5714285714x + x2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + -0.5714285714x + x2 = 0 + 0.05714285714 -0.5714285714x + x2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 -0.5714285714x + x2 = 0.05714285714 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.05714285714 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.05714285714 + 0.08163265305 Combine like terms: 0.05714285714 + 0.08163265305 = 0.13877551019 0.08163265305 + -0.5714285714x + x2 = 0.13877551019 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.13877551019 Calculate the square root of the right side: 0.372525852 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.372525852 and -0.372525852.Subproblem 1
x + -0.2857142857 = 0.372525852 Simplifying x + -0.2857142857 = 0.372525852 Reorder the terms: -0.2857142857 + x = 0.372525852 Solving -0.2857142857 + x = 0.372525852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.372525852 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.372525852 + 0.2857142857 x = 0.372525852 + 0.2857142857 Combine like terms: 0.372525852 + 0.2857142857 = 0.6582401377 x = 0.6582401377 Simplifying x = 0.6582401377Subproblem 2
x + -0.2857142857 = -0.372525852 Simplifying x + -0.2857142857 = -0.372525852 Reorder the terms: -0.2857142857 + x = -0.372525852 Solving -0.2857142857 + x = -0.372525852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.372525852 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.372525852 + 0.2857142857 x = -0.372525852 + 0.2857142857 Combine like terms: -0.372525852 + 0.2857142857 = -0.0868115663 x = -0.0868115663 Simplifying x = -0.0868115663Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6582401377, -0.0868115663}
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