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Simplifying 7x2 + 15x = 205 Reorder the terms: 15x + 7x2 = 205 Solving 15x + 7x2 = 205 Solving for variable 'x'. Reorder the terms: -205 + 15x + 7x2 = 205 + -205 Combine like terms: 205 + -205 = 0 -205 + 15x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -29.28571429 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '29.28571429' to each side of the equation. -29.28571429 + 2.142857143x + 29.28571429 + x2 = 0 + 29.28571429 Reorder the terms: -29.28571429 + 29.28571429 + 2.142857143x + x2 = 0 + 29.28571429 Combine like terms: -29.28571429 + 29.28571429 = 0.00000000 0.00000000 + 2.142857143x + x2 = 0 + 29.28571429 2.142857143x + x2 = 0 + 29.28571429 Combine like terms: 0 + 29.28571429 = 29.28571429 2.142857143x + x2 = 29.28571429 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 = 29.28571429 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = 29.28571429 + 1.147959185 Combine like terms: 29.28571429 + 1.147959185 = 30.433673475 1.147959185 + 2.142857143x + x2 = 30.433673475 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 30.433673475 Calculate the square root of the right side: 5.516672319 Break this problem into two subproblems by setting (x + 1.071428572) equal to 5.516672319 and -5.516672319.Subproblem 1
x + 1.071428572 = 5.516672319 Simplifying x + 1.071428572 = 5.516672319 Reorder the terms: 1.071428572 + x = 5.516672319 Solving 1.071428572 + x = 5.516672319 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 = 5.516672319 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 5.516672319 + -1.071428572 x = 5.516672319 + -1.071428572 Combine like terms: 5.516672319 + -1.071428572 = 4.445243747 x = 4.445243747 Simplifying x = 4.445243747Subproblem 2
x + 1.071428572 = -5.516672319 Simplifying x + 1.071428572 = -5.516672319 Reorder the terms: 1.071428572 + x = -5.516672319 Solving 1.071428572 + x = -5.516672319 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 = -5.516672319 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -5.516672319 + -1.071428572 x = -5.516672319 + -1.071428572 Combine like terms: -5.516672319 + -1.071428572 = -6.588100891 x = -6.588100891 Simplifying x = -6.588100891Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.445243747, -6.588100891}
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