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Simplifying 7x2 + 19x + 10 = 19.38 Reorder the terms: 10 + 19x + 7x2 = 19.38 Solving 10 + 19x + 7x2 = 19.38 Solving for variable 'x'. Reorder the terms: 10 + -19.38 + 19x + 7x2 = 19.38 + -19.38 Combine like terms: 10 + -19.38 = -9.38 -9.38 + 19x + 7x2 = 19.38 + -19.38 Combine like terms: 19.38 + -19.38 = 0.00 -9.38 + 19x + 7x2 = 0.00 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.34 + 2.714285714x + x2 = 0.00 Move the constant term to the right: Add '1.34' to each side of the equation. -1.34 + 2.714285714x + 1.34 + x2 = 0.00 + 1.34 Reorder the terms: -1.34 + 1.34 + 2.714285714x + x2 = 0.00 + 1.34 Combine like terms: -1.34 + 1.34 = 0.00 0.00 + 2.714285714x + x2 = 0.00 + 1.34 2.714285714x + x2 = 0.00 + 1.34 Combine like terms: 0.00 + 1.34 = 1.34 2.714285714x + x2 = 1.34 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 = 1.34 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 1.34 + 1.841836734 Combine like terms: 1.34 + 1.841836734 = 3.181836734 1.841836734 + 2.714285714x + x2 = 3.181836734 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 3.181836734 Calculate the square root of the right side: 1.78377037 Break this problem into two subproblems by setting (x + 1.357142857) equal to 1.78377037 and -1.78377037.Subproblem 1
x + 1.357142857 = 1.78377037 Simplifying x + 1.357142857 = 1.78377037 Reorder the terms: 1.357142857 + x = 1.78377037 Solving 1.357142857 + x = 1.78377037 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 = 1.78377037 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 1.78377037 + -1.357142857 x = 1.78377037 + -1.357142857 Combine like terms: 1.78377037 + -1.357142857 = 0.426627513 x = 0.426627513 Simplifying x = 0.426627513Subproblem 2
x + 1.357142857 = -1.78377037 Simplifying x + 1.357142857 = -1.78377037 Reorder the terms: 1.357142857 + x = -1.78377037 Solving 1.357142857 + x = -1.78377037 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 = -1.78377037 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -1.78377037 + -1.357142857 x = -1.78377037 + -1.357142857 Combine like terms: -1.78377037 + -1.357142857 = -3.140913227 x = -3.140913227 Simplifying x = -3.140913227Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.426627513, -3.140913227}
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