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Simplifying -4.905x2 + 12x + 70 = 0 Reorder the terms: 70 + 12x + -4.905x2 = 0 Solving 70 + 12x + -4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -14.27115189 + -2.44648318x + x2 = 0 Move the constant term to the right: Add '14.27115189' to each side of the equation. -14.27115189 + -2.44648318x + 14.27115189 + x2 = 0 + 14.27115189 Reorder the terms: -14.27115189 + 14.27115189 + -2.44648318x + x2 = 0 + 14.27115189 Combine like terms: -14.27115189 + 14.27115189 = 0.00000000 0.00000000 + -2.44648318x + x2 = 0 + 14.27115189 -2.44648318x + x2 = 0 + 14.27115189 Combine like terms: 0 + 14.27115189 = 14.27115189 -2.44648318x + x2 = 14.27115189 The x term is -2.44648318x. Take half its coefficient (-1.22324159). Square it (1.496319988) and add it to both sides. Add '1.496319988' to each side of the equation. -2.44648318x + 1.496319988 + x2 = 14.27115189 + 1.496319988 Reorder the terms: 1.496319988 + -2.44648318x + x2 = 14.27115189 + 1.496319988 Combine like terms: 14.27115189 + 1.496319988 = 15.767471878 1.496319988 + -2.44648318x + x2 = 15.767471878 Factor a perfect square on the left side: (x + -1.22324159)(x + -1.22324159) = 15.767471878 Calculate the square root of the right side: 3.970827606 Break this problem into two subproblems by setting (x + -1.22324159) equal to 3.970827606 and -3.970827606.Subproblem 1
x + -1.22324159 = 3.970827606 Simplifying x + -1.22324159 = 3.970827606 Reorder the terms: -1.22324159 + x = 3.970827606 Solving -1.22324159 + x = 3.970827606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.22324159' to each side of the equation. -1.22324159 + 1.22324159 + x = 3.970827606 + 1.22324159 Combine like terms: -1.22324159 + 1.22324159 = 0.00000000 0.00000000 + x = 3.970827606 + 1.22324159 x = 3.970827606 + 1.22324159 Combine like terms: 3.970827606 + 1.22324159 = 5.194069196 x = 5.194069196 Simplifying x = 5.194069196Subproblem 2
x + -1.22324159 = -3.970827606 Simplifying x + -1.22324159 = -3.970827606 Reorder the terms: -1.22324159 + x = -3.970827606 Solving -1.22324159 + x = -3.970827606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.22324159' to each side of the equation. -1.22324159 + 1.22324159 + x = -3.970827606 + 1.22324159 Combine like terms: -1.22324159 + 1.22324159 = 0.00000000 0.00000000 + x = -3.970827606 + 1.22324159 x = -3.970827606 + 1.22324159 Combine like terms: -3.970827606 + 1.22324159 = -2.747586016 x = -2.747586016 Simplifying x = -2.747586016Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.194069196, -2.747586016}
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