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Simplifying 5x2 + 3x + -104 = 0 Reorder the terms: -104 + 3x + 5x2 = 0 Solving -104 + 3x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -20.8 + 0.6x + x2 = 0 Move the constant term to the right: Add '20.8' to each side of the equation. -20.8 + 0.6x + 20.8 + x2 = 0 + 20.8 Reorder the terms: -20.8 + 20.8 + 0.6x + x2 = 0 + 20.8 Combine like terms: -20.8 + 20.8 = 0.0 0.0 + 0.6x + x2 = 0 + 20.8 0.6x + x2 = 0 + 20.8 Combine like terms: 0 + 20.8 = 20.8 0.6x + x2 = 20.8 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 20.8 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 20.8 + 0.09 Combine like terms: 20.8 + 0.09 = 20.89 0.09 + 0.6x + x2 = 20.89 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 20.89 Calculate the square root of the right side: 4.570557953 Break this problem into two subproblems by setting (x + 0.3) equal to 4.570557953 and -4.570557953.Subproblem 1
x + 0.3 = 4.570557953 Simplifying x + 0.3 = 4.570557953 Reorder the terms: 0.3 + x = 4.570557953 Solving 0.3 + x = 4.570557953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 4.570557953 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 4.570557953 + -0.3 x = 4.570557953 + -0.3 Combine like terms: 4.570557953 + -0.3 = 4.270557953 x = 4.270557953 Simplifying x = 4.270557953Subproblem 2
x + 0.3 = -4.570557953 Simplifying x + 0.3 = -4.570557953 Reorder the terms: 0.3 + x = -4.570557953 Solving 0.3 + x = -4.570557953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -4.570557953 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -4.570557953 + -0.3 x = -4.570557953 + -0.3 Combine like terms: -4.570557953 + -0.3 = -4.870557953 x = -4.870557953 Simplifying x = -4.870557953Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.270557953, -4.870557953}
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