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Simplifying 7x2 + 15x + -20 = 0 Reorder the terms: -20 + 15x + 7x2 = 0 Solving -20 + 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'. -2.857142857 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + 2.142857143x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + 2.142857143x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + 2.142857143x + x2 = 0 + 2.857142857 2.142857143x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 2.142857143x + x2 = 2.857142857 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 = 2.857142857 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = 2.857142857 + 1.147959185 Combine like terms: 2.857142857 + 1.147959185 = 4.005102042 1.147959185 + 2.142857143x + x2 = 4.005102042 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 4.005102042 Calculate the square root of the right side: 2.001275104 Break this problem into two subproblems by setting (x + 1.071428572) equal to 2.001275104 and -2.001275104.Subproblem 1
x + 1.071428572 = 2.001275104 Simplifying x + 1.071428572 = 2.001275104 Reorder the terms: 1.071428572 + x = 2.001275104 Solving 1.071428572 + x = 2.001275104 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 = 2.001275104 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 2.001275104 + -1.071428572 x = 2.001275104 + -1.071428572 Combine like terms: 2.001275104 + -1.071428572 = 0.929846532 x = 0.929846532 Simplifying x = 0.929846532Subproblem 2
x + 1.071428572 = -2.001275104 Simplifying x + 1.071428572 = -2.001275104 Reorder the terms: 1.071428572 + x = -2.001275104 Solving 1.071428572 + x = -2.001275104 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 = -2.001275104 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -2.001275104 + -1.071428572 x = -2.001275104 + -1.071428572 Combine like terms: -2.001275104 + -1.071428572 = -3.072703676 x = -3.072703676 Simplifying x = -3.072703676Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.929846532, -3.072703676}
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