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Simplifying 7x2 + 15x = 4 Reorder the terms: 15x + 7x2 = 4 Solving 15x + 7x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 15x + 7x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 15x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 2.142857143x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 2.142857143x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 2.142857143x + x2 = 0 + 0.5714285714 2.142857143x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 2.142857143x + x2 = 0.5714285714 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 = 0.5714285714 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = 0.5714285714 + 1.147959185 Combine like terms: 0.5714285714 + 1.147959185 = 1.7193877564 1.147959185 + 2.142857143x + x2 = 1.7193877564 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 1.7193877564 Calculate the square root of the right side: 1.311254268 Break this problem into two subproblems by setting (x + 1.071428572) equal to 1.311254268 and -1.311254268.Subproblem 1
x + 1.071428572 = 1.311254268 Simplifying x + 1.071428572 = 1.311254268 Reorder the terms: 1.071428572 + x = 1.311254268 Solving 1.071428572 + x = 1.311254268 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 = 1.311254268 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 1.311254268 + -1.071428572 x = 1.311254268 + -1.071428572 Combine like terms: 1.311254268 + -1.071428572 = 0.239825696 x = 0.239825696 Simplifying x = 0.239825696Subproblem 2
x + 1.071428572 = -1.311254268 Simplifying x + 1.071428572 = -1.311254268 Reorder the terms: 1.071428572 + x = -1.311254268 Solving 1.071428572 + x = -1.311254268 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 = -1.311254268 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -1.311254268 + -1.071428572 x = -1.311254268 + -1.071428572 Combine like terms: -1.311254268 + -1.071428572 = -2.38268284 x = -2.38268284 Simplifying x = -2.38268284Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.239825696, -2.38268284}
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