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Simplifying 100x2 + 4x + -4.8 = 0 Reorder the terms: -4.8 + 4x + 100x2 = 0 Solving -4.8 + 4x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.048 + 0.04x + x2 = 0 Move the constant term to the right: Add '0.048' to each side of the equation. -0.048 + 0.04x + 0.048 + x2 = 0 + 0.048 Reorder the terms: -0.048 + 0.048 + 0.04x + x2 = 0 + 0.048 Combine like terms: -0.048 + 0.048 = 0.000 0.000 + 0.04x + x2 = 0 + 0.048 0.04x + x2 = 0 + 0.048 Combine like terms: 0 + 0.048 = 0.048 0.04x + x2 = 0.048 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 = 0.048 + 0.0004 Reorder the terms: 0.0004 + 0.04x + x2 = 0.048 + 0.0004 Combine like terms: 0.048 + 0.0004 = 0.0484 0.0004 + 0.04x + x2 = 0.0484 Factor a perfect square on the left side: (x + 0.02)(x + 0.02) = 0.0484 Calculate the square root of the right side: 0.22 Break this problem into two subproblems by setting (x + 0.02) equal to 0.22 and -0.22.Subproblem 1
x + 0.02 = 0.22 Simplifying x + 0.02 = 0.22 Reorder the terms: 0.02 + x = 0.22 Solving 0.02 + x = 0.22 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 = 0.22 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + x = 0.22 + -0.02 x = 0.22 + -0.02 Combine like terms: 0.22 + -0.02 = 0.2 x = 0.2 Simplifying x = 0.2Subproblem 2
x + 0.02 = -0.22 Simplifying x + 0.02 = -0.22 Reorder the terms: 0.02 + x = -0.22 Solving 0.02 + x = -0.22 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 = -0.22 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + x = -0.22 + -0.02 x = -0.22 + -0.02 Combine like terms: -0.22 + -0.02 = -0.24 x = -0.24 Simplifying x = -0.24Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2, -0.24}
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