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Simplifying 7x2 + 19x + -25 = 0 Reorder the terms: -25 + 19x + 7x2 = 0 Solving -25 + 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'. -3.571428571 + 2.714285714x + x2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + 2.714285714x + 3.571428571 + x2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + 2.714285714x + x2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + 2.714285714x + x2 = 0 + 3.571428571 2.714285714x + x2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 2.714285714x + x2 = 3.571428571 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 = 3.571428571 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 3.571428571 + 1.841836734 Combine like terms: 3.571428571 + 1.841836734 = 5.413265305 1.841836734 + 2.714285714x + x2 = 5.413265305 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 5.413265305 Calculate the square root of the right side: 2.326642496 Break this problem into two subproblems by setting (x + 1.357142857) equal to 2.326642496 and -2.326642496.Subproblem 1
x + 1.357142857 = 2.326642496 Simplifying x + 1.357142857 = 2.326642496 Reorder the terms: 1.357142857 + x = 2.326642496 Solving 1.357142857 + x = 2.326642496 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 = 2.326642496 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 2.326642496 + -1.357142857 x = 2.326642496 + -1.357142857 Combine like terms: 2.326642496 + -1.357142857 = 0.969499639 x = 0.969499639 Simplifying x = 0.969499639Subproblem 2
x + 1.357142857 = -2.326642496 Simplifying x + 1.357142857 = -2.326642496 Reorder the terms: 1.357142857 + x = -2.326642496 Solving 1.357142857 + x = -2.326642496 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 = -2.326642496 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -2.326642496 + -1.357142857 x = -2.326642496 + -1.357142857 Combine like terms: -2.326642496 + -1.357142857 = -3.683785353 x = -3.683785353 Simplifying x = -3.683785353Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.969499639, -3.683785353}
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