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Simplifying 0.03x + x2 = 1.5 Solving 0.03x + x2 = 1.5 Solving for variable 'x'. Reorder the terms: -1.5 + 0.03x + x2 = 1.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + 0.03x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.03x + 1.5 + x2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.03x + x2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.03x + x2 = 0.0 + 1.5 0.03x + x2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 0.03x + x2 = 1.5 The x term is 0.03x. Take half its coefficient (0.015). Square it (0.000225) and add it to both sides. Add '0.000225' to each side of the equation. 0.03x + 0.000225 + x2 = 1.5 + 0.000225 Reorder the terms: 0.000225 + 0.03x + x2 = 1.5 + 0.000225 Combine like terms: 1.5 + 0.000225 = 1.500225 0.000225 + 0.03x + x2 = 1.500225 Factor a perfect square on the left side: (x + 0.015)(x + 0.015) = 1.500225 Calculate the square root of the right side: 1.224836724 Break this problem into two subproblems by setting (x + 0.015) equal to 1.224836724 and -1.224836724.Subproblem 1
x + 0.015 = 1.224836724 Simplifying x + 0.015 = 1.224836724 Reorder the terms: 0.015 + x = 1.224836724 Solving 0.015 + x = 1.224836724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015' to each side of the equation. 0.015 + -0.015 + x = 1.224836724 + -0.015 Combine like terms: 0.015 + -0.015 = 0.000 0.000 + x = 1.224836724 + -0.015 x = 1.224836724 + -0.015 Combine like terms: 1.224836724 + -0.015 = 1.209836724 x = 1.209836724 Simplifying x = 1.209836724Subproblem 2
x + 0.015 = -1.224836724 Simplifying x + 0.015 = -1.224836724 Reorder the terms: 0.015 + x = -1.224836724 Solving 0.015 + x = -1.224836724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015' to each side of the equation. 0.015 + -0.015 + x = -1.224836724 + -0.015 Combine like terms: 0.015 + -0.015 = 0.000 0.000 + x = -1.224836724 + -0.015 x = -1.224836724 + -0.015 Combine like terms: -1.224836724 + -0.015 = -1.239836724 x = -1.239836724 Simplifying x = -1.239836724Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.209836724, -1.239836724}
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