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Simplifying x2 + 1.2x + -11.4 = 0 Reorder the terms: -11.4 + 1.2x + x2 = 0 Solving -11.4 + 1.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '11.4' to each side of the equation. -11.4 + 1.2x + 11.4 + x2 = 0 + 11.4 Reorder the terms: -11.4 + 11.4 + 1.2x + x2 = 0 + 11.4 Combine like terms: -11.4 + 11.4 = 0.0 0.0 + 1.2x + x2 = 0 + 11.4 1.2x + x2 = 0 + 11.4 Combine like terms: 0 + 11.4 = 11.4 1.2x + x2 = 11.4 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 11.4 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 11.4 + 0.36 Combine like terms: 11.4 + 0.36 = 11.76 0.36 + 1.2x + x2 = 11.76 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 11.76 Calculate the square root of the right side: 3.42928564 Break this problem into two subproblems by setting (x + 0.6) equal to 3.42928564 and -3.42928564.Subproblem 1
x + 0.6 = 3.42928564 Simplifying x + 0.6 = 3.42928564 Reorder the terms: 0.6 + x = 3.42928564 Solving 0.6 + x = 3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 3.42928564 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 3.42928564 + -0.6 x = 3.42928564 + -0.6 Combine like terms: 3.42928564 + -0.6 = 2.82928564 x = 2.82928564 Simplifying x = 2.82928564Subproblem 2
x + 0.6 = -3.42928564 Simplifying x + 0.6 = -3.42928564 Reorder the terms: 0.6 + x = -3.42928564 Solving 0.6 + x = -3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -3.42928564 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -3.42928564 + -0.6 x = -3.42928564 + -0.6 Combine like terms: -3.42928564 + -0.6 = -4.02928564 x = -4.02928564 Simplifying x = -4.02928564Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.82928564, -4.02928564}
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