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Simplifying 5x2 + 3x + -90 = 0 Reorder the terms: -90 + 3x + 5x2 = 0 Solving -90 + 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'. -18 + 0.6x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 0.6x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 0.6x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 0.6x + x2 = 0 + 18 0.6x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 0.6x + x2 = 18 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 = 18 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 18 + 0.09 Combine like terms: 18 + 0.09 = 18.09 0.09 + 0.6x + x2 = 18.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 18.09 Calculate the square root of the right side: 4.253234064 Break this problem into two subproblems by setting (x + 0.3) equal to 4.253234064 and -4.253234064.Subproblem 1
x + 0.3 = 4.253234064 Simplifying x + 0.3 = 4.253234064 Reorder the terms: 0.3 + x = 4.253234064 Solving 0.3 + x = 4.253234064 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 = 4.253234064 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 4.253234064 + -0.3 x = 4.253234064 + -0.3 Combine like terms: 4.253234064 + -0.3 = 3.953234064 x = 3.953234064 Simplifying x = 3.953234064Subproblem 2
x + 0.3 = -4.253234064 Simplifying x + 0.3 = -4.253234064 Reorder the terms: 0.3 + x = -4.253234064 Solving 0.3 + x = -4.253234064 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 = -4.253234064 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -4.253234064 + -0.3 x = -4.253234064 + -0.3 Combine like terms: -4.253234064 + -0.3 = -4.553234064 x = -4.553234064 Simplifying x = -4.553234064Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.953234064, -4.553234064}
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