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Simplifying 0 = 7x2 + -15x + -7 Reorder the terms: 0 = -7 + -15x + 7x2 Solving 0 = -7 + -15x + 7x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + 15x + -7x2 = -7 + -15x + 7x2 + 7 + 15x + -7x2 Reorder the terms: 7 + 15x + -7x2 = -7 + 7 + -15x + 15x + 7x2 + -7x2 Combine like terms: -7 + 7 = 0 7 + 15x + -7x2 = 0 + -15x + 15x + 7x2 + -7x2 7 + 15x + -7x2 = -15x + 15x + 7x2 + -7x2 Combine like terms: -15x + 15x = 0 7 + 15x + -7x2 = 0 + 7x2 + -7x2 7 + 15x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 7 + 15x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1 + -2.142857143x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.142857143x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.142857143x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.142857143x + x2 = 0 + 1 -2.142857143x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.142857143x + x2 = 1 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 = 1 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143x + x2 = 1 + 1.147959185 Combine like terms: 1 + 1.147959185 = 2.147959185 1.147959185 + -2.142857143x + x2 = 2.147959185 Factor a perfect square on the left side: (x + -1.071428572)(x + -1.071428572) = 2.147959185 Calculate the square root of the right side: 1.465591753 Break this problem into two subproblems by setting (x + -1.071428572) equal to 1.465591753 and -1.465591753.Subproblem 1
x + -1.071428572 = 1.465591753 Simplifying x + -1.071428572 = 1.465591753 Reorder the terms: -1.071428572 + x = 1.465591753 Solving -1.071428572 + x = 1.465591753 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 = 1.465591753 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 1.465591753 + 1.071428572 x = 1.465591753 + 1.071428572 Combine like terms: 1.465591753 + 1.071428572 = 2.537020325 x = 2.537020325 Simplifying x = 2.537020325Subproblem 2
x + -1.071428572 = -1.465591753 Simplifying x + -1.071428572 = -1.465591753 Reorder the terms: -1.071428572 + x = -1.465591753 Solving -1.071428572 + x = -1.465591753 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 = -1.465591753 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -1.465591753 + 1.071428572 x = -1.465591753 + 1.071428572 Combine like terms: -1.465591753 + 1.071428572 = -0.394163181 x = -0.394163181 Simplifying x = -0.394163181Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.537020325, -0.394163181}
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