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Simplifying x2 + 0.43x + -34.4 = 0 Reorder the terms: -34.4 + 0.43x + x2 = 0 Solving -34.4 + 0.43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '34.4' to each side of the equation. -34.4 + 0.43x + 34.4 + x2 = 0 + 34.4 Reorder the terms: -34.4 + 34.4 + 0.43x + x2 = 0 + 34.4 Combine like terms: -34.4 + 34.4 = 0.0 0.0 + 0.43x + x2 = 0 + 34.4 0.43x + x2 = 0 + 34.4 Combine like terms: 0 + 34.4 = 34.4 0.43x + x2 = 34.4 The x term is 0.43x. Take half its coefficient (0.215). Square it (0.046225) and add it to both sides. Add '0.046225' to each side of the equation. 0.43x + 0.046225 + x2 = 34.4 + 0.046225 Reorder the terms: 0.046225 + 0.43x + x2 = 34.4 + 0.046225 Combine like terms: 34.4 + 0.046225 = 34.446225 0.046225 + 0.43x + x2 = 34.446225 Factor a perfect square on the left side: (x + 0.215)(x + 0.215) = 34.446225 Calculate the square root of the right side: 5.869090645 Break this problem into two subproblems by setting (x + 0.215) equal to 5.869090645 and -5.869090645.Subproblem 1
x + 0.215 = 5.869090645 Simplifying x + 0.215 = 5.869090645 Reorder the terms: 0.215 + x = 5.869090645 Solving 0.215 + x = 5.869090645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.215' to each side of the equation. 0.215 + -0.215 + x = 5.869090645 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = 5.869090645 + -0.215 x = 5.869090645 + -0.215 Combine like terms: 5.869090645 + -0.215 = 5.654090645 x = 5.654090645 Simplifying x = 5.654090645Subproblem 2
x + 0.215 = -5.869090645 Simplifying x + 0.215 = -5.869090645 Reorder the terms: 0.215 + x = -5.869090645 Solving 0.215 + x = -5.869090645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.215' to each side of the equation. 0.215 + -0.215 + x = -5.869090645 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = -5.869090645 + -0.215 x = -5.869090645 + -0.215 Combine like terms: -5.869090645 + -0.215 = -6.084090645 x = -6.084090645 Simplifying x = -6.084090645Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.654090645, -6.084090645}
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