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Simplifying x2 + 1.30x + -12 = 0 Reorder the terms: -12 + 1.30x + x2 = 0 Solving -12 + 1.30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 1.30x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 1.30x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 1.30x + x2 = 0 + 12 1.30x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 1.30x + x2 = 12 The x term is 1.30x. Take half its coefficient (0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. 1.30x + 0.4225 + x2 = 12 + 0.4225 Reorder the terms: 0.4225 + 1.30x + x2 = 12 + 0.4225 Combine like terms: 12 + 0.4225 = 12.4225 0.4225 + 1.30x + x2 = 12.4225 Factor a perfect square on the left side: (x + 0.65)(x + 0.65) = 12.4225 Calculate the square root of the right side: 3.52455671 Break this problem into two subproblems by setting (x + 0.65) equal to 3.52455671 and -3.52455671.Subproblem 1
x + 0.65 = 3.52455671 Simplifying x + 0.65 = 3.52455671 Reorder the terms: 0.65 + x = 3.52455671 Solving 0.65 + x = 3.52455671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = 3.52455671 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = 3.52455671 + -0.65 x = 3.52455671 + -0.65 Combine like terms: 3.52455671 + -0.65 = 2.87455671 x = 2.87455671 Simplifying x = 2.87455671Subproblem 2
x + 0.65 = -3.52455671 Simplifying x + 0.65 = -3.52455671 Reorder the terms: 0.65 + x = -3.52455671 Solving 0.65 + x = -3.52455671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = -3.52455671 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = -3.52455671 + -0.65 x = -3.52455671 + -0.65 Combine like terms: -3.52455671 + -0.65 = -4.17455671 x = -4.17455671 Simplifying x = -4.17455671Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.87455671, -4.17455671}
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