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Simplifying 7x2 + 30x = -19 Reorder the terms: 30x + 7x2 = -19 Solving 30x + 7x2 = -19 Solving for variable 'x'. Reorder the terms: 19 + 30x + 7x2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + 30x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.714285714 + 4.285714286x + x2 = 0 Move the constant term to the right: Add '-2.714285714' to each side of the equation. 2.714285714 + 4.285714286x + -2.714285714 + x2 = 0 + -2.714285714 Reorder the terms: 2.714285714 + -2.714285714 + 4.285714286x + x2 = 0 + -2.714285714 Combine like terms: 2.714285714 + -2.714285714 = 0.000000000 0.000000000 + 4.285714286x + x2 = 0 + -2.714285714 4.285714286x + x2 = 0 + -2.714285714 Combine like terms: 0 + -2.714285714 = -2.714285714 4.285714286x + x2 = -2.714285714 The x term is 4.285714286x. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286x + 4.591836735 + x2 = -2.714285714 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286x + x2 = -2.714285714 + 4.591836735 Combine like terms: -2.714285714 + 4.591836735 = 1.877551021 4.591836735 + 4.285714286x + x2 = 1.877551021 Factor a perfect square on the left side: (x + 2.142857143)(x + 2.142857143) = 1.877551021 Calculate the square root of the right side: 1.370237578 Break this problem into two subproblems by setting (x + 2.142857143) equal to 1.370237578 and -1.370237578.Subproblem 1
x + 2.142857143 = 1.370237578 Simplifying x + 2.142857143 = 1.370237578 Reorder the terms: 2.142857143 + x = 1.370237578 Solving 2.142857143 + x = 1.370237578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = 1.370237578 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = 1.370237578 + -2.142857143 x = 1.370237578 + -2.142857143 Combine like terms: 1.370237578 + -2.142857143 = -0.772619565 x = -0.772619565 Simplifying x = -0.772619565Subproblem 2
x + 2.142857143 = -1.370237578 Simplifying x + 2.142857143 = -1.370237578 Reorder the terms: 2.142857143 + x = -1.370237578 Solving 2.142857143 + x = -1.370237578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = -1.370237578 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = -1.370237578 + -2.142857143 x = -1.370237578 + -2.142857143 Combine like terms: -1.370237578 + -2.142857143 = -3.513094721 x = -3.513094721 Simplifying x = -3.513094721Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.772619565, -3.513094721}
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