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Simplifying 7x2 + -19x + -10 = 19.4 Reorder the terms: -10 + -19x + 7x2 = 19.4 Solving -10 + -19x + 7x2 = 19.4 Solving for variable 'x'. Reorder the terms: -10 + -19.4 + -19x + 7x2 = 19.4 + -19.4 Combine like terms: -10 + -19.4 = -29.4 -29.4 + -19x + 7x2 = 19.4 + -19.4 Combine like terms: 19.4 + -19.4 = 0.0 -29.4 + -19x + 7x2 = 0.0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.2 + -2.714285714x + x2 = 0.0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -2.714285714x + 4.2 + x2 = 0.0 + 4.2 Reorder the terms: -4.2 + 4.2 + -2.714285714x + x2 = 0.0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -2.714285714x + x2 = 0.0 + 4.2 -2.714285714x + x2 = 0.0 + 4.2 Combine like terms: 0.0 + 4.2 = 4.2 -2.714285714x + x2 = 4.2 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 = 4.2 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714x + x2 = 4.2 + 1.841836734 Combine like terms: 4.2 + 1.841836734 = 6.041836734 1.841836734 + -2.714285714x + x2 = 6.041836734 Factor a perfect square on the left side: (x + -1.357142857)(x + -1.357142857) = 6.041836734 Calculate the square root of the right side: 2.458014795 Break this problem into two subproblems by setting (x + -1.357142857) equal to 2.458014795 and -2.458014795.Subproblem 1
x + -1.357142857 = 2.458014795 Simplifying x + -1.357142857 = 2.458014795 Reorder the terms: -1.357142857 + x = 2.458014795 Solving -1.357142857 + x = 2.458014795 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 = 2.458014795 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 2.458014795 + 1.357142857 x = 2.458014795 + 1.357142857 Combine like terms: 2.458014795 + 1.357142857 = 3.815157652 x = 3.815157652 Simplifying x = 3.815157652Subproblem 2
x + -1.357142857 = -2.458014795 Simplifying x + -1.357142857 = -2.458014795 Reorder the terms: -1.357142857 + x = -2.458014795 Solving -1.357142857 + x = -2.458014795 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 = -2.458014795 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -2.458014795 + 1.357142857 x = -2.458014795 + 1.357142857 Combine like terms: -2.458014795 + 1.357142857 = -1.100871938 x = -1.100871938 Simplifying x = -1.100871938Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.815157652, -1.100871938}
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