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Simplifying x2 + 70x + 24 = 0 Reorder the terms: 24 + 70x + x2 = 0 Solving 24 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 70x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 70x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 70x + x2 = 0 + -24 70x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 70x + x2 = -24 The x term is 70x. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70x + 1225 + x2 = -24 + 1225 Reorder the terms: 1225 + 70x + x2 = -24 + 1225 Combine like terms: -24 + 1225 = 1201 1225 + 70x + x2 = 1201 Factor a perfect square on the left side: (x + 35)(x + 35) = 1201 Calculate the square root of the right side: 34.655446902 Break this problem into two subproblems by setting (x + 35) equal to 34.655446902 and -34.655446902.Subproblem 1
x + 35 = 34.655446902 Simplifying x + 35 = 34.655446902 Reorder the terms: 35 + x = 34.655446902 Solving 35 + x = 34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 34.655446902 + -35 Combine like terms: 35 + -35 = 0 0 + x = 34.655446902 + -35 x = 34.655446902 + -35 Combine like terms: 34.655446902 + -35 = -0.344553098 x = -0.344553098 Simplifying x = -0.344553098Subproblem 2
x + 35 = -34.655446902 Simplifying x + 35 = -34.655446902 Reorder the terms: 35 + x = -34.655446902 Solving 35 + x = -34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = -34.655446902 + -35 Combine like terms: 35 + -35 = 0 0 + x = -34.655446902 + -35 x = -34.655446902 + -35 Combine like terms: -34.655446902 + -35 = -69.655446902 x = -69.655446902 Simplifying x = -69.655446902Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.344553098, -69.655446902}
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