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Simplifying x2 + 2x(0.6) = 0.45 Reorder the terms for easier multiplication: x2 + 2 * 0.6x = 0.45 Multiply 2 * 0.6 x2 + 1.2x = 0.45 Reorder the terms: 1.2x + x2 = 0.45 Solving 1.2x + x2 = 0.45 Solving for variable 'x'. Reorder the terms: -0.45 + 1.2x + x2 = 0.45 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 -0.45 + 1.2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 1.2x + 0.45 + x2 = 0.00 + 0.45 Reorder the terms: -0.45 + 0.45 + 1.2x + x2 = 0.00 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 1.2x + x2 = 0.00 + 0.45 1.2x + x2 = 0.00 + 0.45 Combine like terms: 0.00 + 0.45 = 0.45 1.2x + x2 = 0.45 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 = 0.45 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.45 + 0.36 Combine like terms: 0.45 + 0.36 = 0.81 0.36 + 1.2x + x2 = 0.81 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.81 Calculate the square root of the right side: 0.9 Break this problem into two subproblems by setting (x + 0.6) equal to 0.9 and -0.9.Subproblem 1
x + 0.6 = 0.9 Simplifying x + 0.6 = 0.9 Reorder the terms: 0.6 + x = 0.9 Solving 0.6 + x = 0.9 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 = 0.9 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.9 + -0.6 x = 0.9 + -0.6 Combine like terms: 0.9 + -0.6 = 0.3 x = 0.3 Simplifying x = 0.3Subproblem 2
x + 0.6 = -0.9 Simplifying x + 0.6 = -0.9 Reorder the terms: 0.6 + x = -0.9 Solving 0.6 + x = -0.9 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 = -0.9 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.9 + -0.6 x = -0.9 + -0.6 Combine like terms: -0.9 + -0.6 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3, -1.5}
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