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Simplifying 7x2 + 15x + -30 = 0 Reorder the terms: -30 + 15x + 7x2 = 0 Solving -30 + 15x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.285714286 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + 2.142857143x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + 2.142857143x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + 2.142857143x + x2 = 0 + 4.285714286 2.142857143x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 2.142857143x + x2 = 4.285714286 The x term is 2.142857143x. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143x + 1.147959185 + x2 = 4.285714286 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = 4.285714286 + 1.147959185 Combine like terms: 4.285714286 + 1.147959185 = 5.433673471 1.147959185 + 2.142857143x + x2 = 5.433673471 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 5.433673471 Calculate the square root of the right side: 2.331024125 Break this problem into two subproblems by setting (x + 1.071428572) equal to 2.331024125 and -2.331024125.Subproblem 1
x + 1.071428572 = 2.331024125 Simplifying x + 1.071428572 = 2.331024125 Reorder the terms: 1.071428572 + x = 2.331024125 Solving 1.071428572 + x = 2.331024125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = 2.331024125 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 2.331024125 + -1.071428572 x = 2.331024125 + -1.071428572 Combine like terms: 2.331024125 + -1.071428572 = 1.259595553 x = 1.259595553 Simplifying x = 1.259595553Subproblem 2
x + 1.071428572 = -2.331024125 Simplifying x + 1.071428572 = -2.331024125 Reorder the terms: 1.071428572 + x = -2.331024125 Solving 1.071428572 + x = -2.331024125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = -2.331024125 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -2.331024125 + -1.071428572 x = -2.331024125 + -1.071428572 Combine like terms: -2.331024125 + -1.071428572 = -3.402452697 x = -3.402452697 Simplifying x = -3.402452697Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.259595553, -3.402452697}
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