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Simplifying 4.05x2 + 15x + 2 = 0 Reorder the terms: 2 + 15x + 4.05x2 = 0 Solving 2 + 15x + 4.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.05 the coefficient of the squared term: Divide each side by '4.05'. 0.4938271605 + 3.703703704x + x2 = 0 Move the constant term to the right: Add '-0.4938271605' to each side of the equation. 0.4938271605 + 3.703703704x + -0.4938271605 + x2 = 0 + -0.4938271605 Reorder the terms: 0.4938271605 + -0.4938271605 + 3.703703704x + x2 = 0 + -0.4938271605 Combine like terms: 0.4938271605 + -0.4938271605 = 0.0000000000 0.0000000000 + 3.703703704x + x2 = 0 + -0.4938271605 3.703703704x + x2 = 0 + -0.4938271605 Combine like terms: 0 + -0.4938271605 = -0.4938271605 3.703703704x + x2 = -0.4938271605 The x term is 3.703703704x. Take half its coefficient (1.851851852). Square it (3.429355282) and add it to both sides. Add '3.429355282' to each side of the equation. 3.703703704x + 3.429355282 + x2 = -0.4938271605 + 3.429355282 Reorder the terms: 3.429355282 + 3.703703704x + x2 = -0.4938271605 + 3.429355282 Combine like terms: -0.4938271605 + 3.429355282 = 2.9355281215 3.429355282 + 3.703703704x + x2 = 2.9355281215 Factor a perfect square on the left side: (x + 1.851851852)(x + 1.851851852) = 2.9355281215 Calculate the square root of the right side: 1.713338297 Break this problem into two subproblems by setting (x + 1.851851852) equal to 1.713338297 and -1.713338297.Subproblem 1
x + 1.851851852 = 1.713338297 Simplifying x + 1.851851852 = 1.713338297 Reorder the terms: 1.851851852 + x = 1.713338297 Solving 1.851851852 + x = 1.713338297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.851851852' to each side of the equation. 1.851851852 + -1.851851852 + x = 1.713338297 + -1.851851852 Combine like terms: 1.851851852 + -1.851851852 = 0.000000000 0.000000000 + x = 1.713338297 + -1.851851852 x = 1.713338297 + -1.851851852 Combine like terms: 1.713338297 + -1.851851852 = -0.138513555 x = -0.138513555 Simplifying x = -0.138513555Subproblem 2
x + 1.851851852 = -1.713338297 Simplifying x + 1.851851852 = -1.713338297 Reorder the terms: 1.851851852 + x = -1.713338297 Solving 1.851851852 + x = -1.713338297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.851851852' to each side of the equation. 1.851851852 + -1.851851852 + x = -1.713338297 + -1.851851852 Combine like terms: 1.851851852 + -1.851851852 = 0.000000000 0.000000000 + x = -1.713338297 + -1.851851852 x = -1.713338297 + -1.851851852 Combine like terms: -1.713338297 + -1.851851852 = -3.565190149 x = -3.565190149 Simplifying x = -3.565190149Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.138513555, -3.565190149}
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