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Simplifying 0 = 7x2 + -15x + -2 Reorder the terms: 0 = -2 + -15x + 7x2 Solving 0 = -2 + -15x + 7x2 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + 15x + -7x2 = -2 + -15x + 7x2 + 2 + 15x + -7x2 Reorder the terms: 2 + 15x + -7x2 = -2 + 2 + -15x + 15x + 7x2 + -7x2 Combine like terms: -2 + 2 = 0 2 + 15x + -7x2 = 0 + -15x + 15x + 7x2 + -7x2 2 + 15x + -7x2 = -15x + 15x + 7x2 + -7x2 Combine like terms: -15x + 15x = 0 2 + 15x + -7x2 = 0 + 7x2 + -7x2 2 + 15x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 2 + 15x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.2857142857 + -2.142857143x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -2.142857143x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -2.142857143x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -2.142857143x + x2 = 0 + 0.2857142857 -2.142857143x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -2.142857143x + x2 = 0.2857142857 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 = 0.2857142857 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143x + x2 = 0.2857142857 + 1.147959185 Combine like terms: 0.2857142857 + 1.147959185 = 1.4336734707 1.147959185 + -2.142857143x + x2 = 1.4336734707 Factor a perfect square on the left side: (x + -1.071428572)(x + -1.071428572) = 1.4336734707 Calculate the square root of the right side: 1.197361044 Break this problem into two subproblems by setting (x + -1.071428572) equal to 1.197361044 and -1.197361044.Subproblem 1
x + -1.071428572 = 1.197361044 Simplifying x + -1.071428572 = 1.197361044 Reorder the terms: -1.071428572 + x = 1.197361044 Solving -1.071428572 + x = 1.197361044 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 = 1.197361044 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 1.197361044 + 1.071428572 x = 1.197361044 + 1.071428572 Combine like terms: 1.197361044 + 1.071428572 = 2.268789616 x = 2.268789616 Simplifying x = 2.268789616Subproblem 2
x + -1.071428572 = -1.197361044 Simplifying x + -1.071428572 = -1.197361044 Reorder the terms: -1.071428572 + x = -1.197361044 Solving -1.071428572 + x = -1.197361044 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 = -1.197361044 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -1.197361044 + 1.071428572 x = -1.197361044 + 1.071428572 Combine like terms: -1.197361044 + 1.071428572 = -0.125932472 x = -0.125932472 Simplifying x = -0.125932472Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.268789616, -0.125932472}
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