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Simplifying 7x2 + -19x + 10 = 20 Reorder the terms: 10 + -19x + 7x2 = 20 Solving 10 + -19x + 7x2 = 20 Solving for variable 'x'. Reorder the terms: 10 + -20 + -19x + 7x2 = 20 + -20 Combine like terms: 10 + -20 = -10 -10 + -19x + 7x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -10 + -19x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + -2.714285714x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -2.714285714x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -2.714285714x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -2.714285714x + x2 = 0 + 1.428571429 -2.714285714x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -2.714285714x + x2 = 1.428571429 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 = 1.428571429 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714x + x2 = 1.428571429 + 1.841836734 Combine like terms: 1.428571429 + 1.841836734 = 3.270408163 1.841836734 + -2.714285714x + x2 = 3.270408163 Factor a perfect square on the left side: (x + -1.357142857)(x + -1.357142857) = 3.270408163 Calculate the square root of the right side: 1.808426986 Break this problem into two subproblems by setting (x + -1.357142857) equal to 1.808426986 and -1.808426986.Subproblem 1
x + -1.357142857 = 1.808426986 Simplifying x + -1.357142857 = 1.808426986 Reorder the terms: -1.357142857 + x = 1.808426986 Solving -1.357142857 + x = 1.808426986 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 = 1.808426986 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = 1.808426986 + 1.357142857 x = 1.808426986 + 1.357142857 Combine like terms: 1.808426986 + 1.357142857 = 3.165569843 x = 3.165569843 Simplifying x = 3.165569843Subproblem 2
x + -1.357142857 = -1.808426986 Simplifying x + -1.357142857 = -1.808426986 Reorder the terms: -1.357142857 + x = -1.808426986 Solving -1.357142857 + x = -1.808426986 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 = -1.808426986 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + x = -1.808426986 + 1.357142857 x = -1.808426986 + 1.357142857 Combine like terms: -1.808426986 + 1.357142857 = -0.451284129 x = -0.451284129 Simplifying x = -0.451284129Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.165569843, -0.451284129}
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