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Simplifying x2 + 5.3x + -1 = 0 Reorder the terms: -1 + 5.3x + x2 = 0 Solving -1 + 5.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 5.3x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 5.3x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5.3x + x2 = 0 + 1 5.3x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 5.3x + x2 = 1 The x term is 5.3x. Take half its coefficient (2.65). Square it (7.0225) and add it to both sides. Add '7.0225' to each side of the equation. 5.3x + 7.0225 + x2 = 1 + 7.0225 Reorder the terms: 7.0225 + 5.3x + x2 = 1 + 7.0225 Combine like terms: 1 + 7.0225 = 8.0225 7.0225 + 5.3x + x2 = 8.0225 Factor a perfect square on the left side: (x + 2.65)(x + 2.65) = 8.0225 Calculate the square root of the right side: 2.832401808 Break this problem into two subproblems by setting (x + 2.65) equal to 2.832401808 and -2.832401808.Subproblem 1
x + 2.65 = 2.832401808 Simplifying x + 2.65 = 2.832401808 Reorder the terms: 2.65 + x = 2.832401808 Solving 2.65 + x = 2.832401808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.65' to each side of the equation. 2.65 + -2.65 + x = 2.832401808 + -2.65 Combine like terms: 2.65 + -2.65 = 0.00 0.00 + x = 2.832401808 + -2.65 x = 2.832401808 + -2.65 Combine like terms: 2.832401808 + -2.65 = 0.182401808 x = 0.182401808 Simplifying x = 0.182401808Subproblem 2
x + 2.65 = -2.832401808 Simplifying x + 2.65 = -2.832401808 Reorder the terms: 2.65 + x = -2.832401808 Solving 2.65 + x = -2.832401808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.65' to each side of the equation. 2.65 + -2.65 + x = -2.832401808 + -2.65 Combine like terms: 2.65 + -2.65 = 0.00 0.00 + x = -2.832401808 + -2.65 x = -2.832401808 + -2.65 Combine like terms: -2.832401808 + -2.65 = -5.482401808 x = -5.482401808 Simplifying x = -5.482401808Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.182401808, -5.482401808}
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