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Simplifying x2 + 28x + -770 = 0 Reorder the terms: -770 + 28x + x2 = 0 Solving -770 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '770' to each side of the equation. -770 + 28x + 770 + x2 = 0 + 770 Reorder the terms: -770 + 770 + 28x + x2 = 0 + 770 Combine like terms: -770 + 770 = 0 0 + 28x + x2 = 0 + 770 28x + x2 = 0 + 770 Combine like terms: 0 + 770 = 770 28x + x2 = 770 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 770 + 196 Reorder the terms: 196 + 28x + x2 = 770 + 196 Combine like terms: 770 + 196 = 966 196 + 28x + x2 = 966 Factor a perfect square on the left side: (x + 14)(x + 14) = 966 Calculate the square root of the right side: 31.080540536 Break this problem into two subproblems by setting (x + 14) equal to 31.080540536 and -31.080540536.Subproblem 1
x + 14 = 31.080540536 Simplifying x + 14 = 31.080540536 Reorder the terms: 14 + x = 31.080540536 Solving 14 + x = 31.080540536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 31.080540536 + -14 Combine like terms: 14 + -14 = 0 0 + x = 31.080540536 + -14 x = 31.080540536 + -14 Combine like terms: 31.080540536 + -14 = 17.080540536 x = 17.080540536 Simplifying x = 17.080540536Subproblem 2
x + 14 = -31.080540536 Simplifying x + 14 = -31.080540536 Reorder the terms: 14 + x = -31.080540536 Solving 14 + x = -31.080540536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -31.080540536 + -14 Combine like terms: 14 + -14 = 0 0 + x = -31.080540536 + -14 x = -31.080540536 + -14 Combine like terms: -31.080540536 + -14 = -45.080540536 x = -45.080540536 Simplifying x = -45.080540536Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.080540536, -45.080540536}
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