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Simplifying 5x2 + 3x = 400 Reorder the terms: 3x + 5x2 = 400 Solving 3x + 5x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 3x + 5x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -80 + 0.6x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 0.6x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 0.6x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 0.6x + x2 = 0 + 80 0.6x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 0.6x + x2 = 80 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 = 80 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 80 + 0.09 Combine like terms: 80 + 0.09 = 80.09 0.09 + 0.6x + x2 = 80.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 80.09 Calculate the square root of the right side: 8.949301649 Break this problem into two subproblems by setting (x + 0.3) equal to 8.949301649 and -8.949301649.Subproblem 1
x + 0.3 = 8.949301649 Simplifying x + 0.3 = 8.949301649 Reorder the terms: 0.3 + x = 8.949301649 Solving 0.3 + x = 8.949301649 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 = 8.949301649 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 8.949301649 + -0.3 x = 8.949301649 + -0.3 Combine like terms: 8.949301649 + -0.3 = 8.649301649 x = 8.649301649 Simplifying x = 8.649301649Subproblem 2
x + 0.3 = -8.949301649 Simplifying x + 0.3 = -8.949301649 Reorder the terms: 0.3 + x = -8.949301649 Solving 0.3 + x = -8.949301649 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 = -8.949301649 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -8.949301649 + -0.3 x = -8.949301649 + -0.3 Combine like terms: -8.949301649 + -0.3 = -9.249301649 x = -9.249301649 Simplifying x = -9.249301649Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.649301649, -9.249301649}
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