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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 = -9.4 -9.4 + 19x + 7x2 = 19.4 + -19.4 Combine like terms: 19.4 + -19.4 = 0.0 -9.4 + 19x + 7x2 = 0.0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.342857143 + 2.714285714x + x2 = 0.0 Move the constant term to the right: Add '1.342857143' to each side of the equation. -1.342857143 + 2.714285714x + 1.342857143 + x2 = 0.0 + 1.342857143 Reorder the terms: -1.342857143 + 1.342857143 + 2.714285714x + x2 = 0.0 + 1.342857143 Combine like terms: -1.342857143 + 1.342857143 = 0.000000000 0.000000000 + 2.714285714x + x2 = 0.0 + 1.342857143 2.714285714x + x2 = 0.0 + 1.342857143 Combine like terms: 0.0 + 1.342857143 = 1.342857143 2.714285714x + x2 = 1.342857143 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 = 1.342857143 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 1.342857143 + 1.841836734 Combine like terms: 1.342857143 + 1.841836734 = 3.184693877 1.841836734 + 2.714285714x + x2 = 3.184693877 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 3.184693877 Calculate the square root of the right side: 1.784571062 Break this problem into two subproblems by setting (x + 1.357142857) equal to 1.784571062 and -1.784571062.Subproblem 1
x + 1.357142857 = 1.784571062 Simplifying x + 1.357142857 = 1.784571062 Reorder the terms: 1.357142857 + x = 1.784571062 Solving 1.357142857 + x = 1.784571062 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 = 1.784571062 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 1.784571062 + -1.357142857 x = 1.784571062 + -1.357142857 Combine like terms: 1.784571062 + -1.357142857 = 0.427428205 x = 0.427428205 Simplifying x = 0.427428205Subproblem 2
x + 1.357142857 = -1.784571062 Simplifying x + 1.357142857 = -1.784571062 Reorder the terms: 1.357142857 + x = -1.784571062 Solving 1.357142857 + x = -1.784571062 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 = -1.784571062 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -1.784571062 + -1.357142857 x = -1.784571062 + -1.357142857 Combine like terms: -1.784571062 + -1.357142857 = -3.141713919 x = -3.141713919 Simplifying x = -3.141713919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.427428205, -3.141713919}
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