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Simplifying 7x2 + 19x + -5 = 0 Reorder the terms: -5 + 19x + 7x2 = 0 Solving -5 + 19x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 2.714285714x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 2.714285714x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 2.714285714x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 2.714285714x + x2 = 0 + 0.7142857143 2.714285714x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 2.714285714x + x2 = 0.7142857143 The x term is 2.714285714x. Take half its coefficient (1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. 2.714285714x + 1.841836734 + x2 = 0.7142857143 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 0.7142857143 + 1.841836734 Combine like terms: 0.7142857143 + 1.841836734 = 2.5561224483 1.841836734 + 2.714285714x + x2 = 2.5561224483 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 2.5561224483 Calculate the square root of the right side: 1.598787806 Break this problem into two subproblems by setting (x + 1.357142857) equal to 1.598787806 and -1.598787806.Subproblem 1
x + 1.357142857 = 1.598787806 Simplifying x + 1.357142857 = 1.598787806 Reorder the terms: 1.357142857 + x = 1.598787806 Solving 1.357142857 + x = 1.598787806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + x = 1.598787806 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 1.598787806 + -1.357142857 x = 1.598787806 + -1.357142857 Combine like terms: 1.598787806 + -1.357142857 = 0.241644949 x = 0.241644949 Simplifying x = 0.241644949Subproblem 2
x + 1.357142857 = -1.598787806 Simplifying x + 1.357142857 = -1.598787806 Reorder the terms: 1.357142857 + x = -1.598787806 Solving 1.357142857 + x = -1.598787806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + x = -1.598787806 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -1.598787806 + -1.357142857 x = -1.598787806 + -1.357142857 Combine like terms: -1.598787806 + -1.357142857 = -2.955930663 x = -2.955930663 Simplifying x = -2.955930663Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.241644949, -2.955930663}
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