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Simplifying 3.5x2 + -0.14x + -0.0049 = 0 Reorder the terms: -0.0049 + -0.14x + 3.5x2 = 0 Solving -0.0049 + -0.14x + 3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -0.0014 + -0.04x + x2 = 0 Move the constant term to the right: Add '0.0014' to each side of the equation. -0.0014 + -0.04x + 0.0014 + x2 = 0 + 0.0014 Reorder the terms: -0.0014 + 0.0014 + -0.04x + x2 = 0 + 0.0014 Combine like terms: -0.0014 + 0.0014 = 0.0000 0.0000 + -0.04x + x2 = 0 + 0.0014 -0.04x + x2 = 0 + 0.0014 Combine like terms: 0 + 0.0014 = 0.0014 -0.04x + x2 = 0.0014 The x term is -0.04x. Take half its coefficient (-0.02). Square it (0.0004) and add it to both sides. Add '0.0004' to each side of the equation. -0.04x + 0.0004 + x2 = 0.0014 + 0.0004 Reorder the terms: 0.0004 + -0.04x + x2 = 0.0014 + 0.0004 Combine like terms: 0.0014 + 0.0004 = 0.0018 0.0004 + -0.04x + x2 = 0.0018 Factor a perfect square on the left side: (x + -0.02)(x + -0.02) = 0.0018 Calculate the square root of the right side: 0.042426407 Break this problem into two subproblems by setting (x + -0.02) equal to 0.042426407 and -0.042426407.Subproblem 1
x + -0.02 = 0.042426407 Simplifying x + -0.02 = 0.042426407 Reorder the terms: -0.02 + x = 0.042426407 Solving -0.02 + x = 0.042426407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = 0.042426407 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = 0.042426407 + 0.02 x = 0.042426407 + 0.02 Combine like terms: 0.042426407 + 0.02 = 0.062426407 x = 0.062426407 Simplifying x = 0.062426407Subproblem 2
x + -0.02 = -0.042426407 Simplifying x + -0.02 = -0.042426407 Reorder the terms: -0.02 + x = -0.042426407 Solving -0.02 + x = -0.042426407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = -0.042426407 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = -0.042426407 + 0.02 x = -0.042426407 + 0.02 Combine like terms: -0.042426407 + 0.02 = -0.022426407 x = -0.022426407 Simplifying x = -0.022426407Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.062426407, -0.022426407}
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