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Simplifying 5x2 + 3x + -89 = 0 Reorder the terms: -89 + 3x + 5x2 = 0 Solving -89 + 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'. -17.8 + 0.6x + x2 = 0 Move the constant term to the right: Add '17.8' to each side of the equation. -17.8 + 0.6x + 17.8 + x2 = 0 + 17.8 Reorder the terms: -17.8 + 17.8 + 0.6x + x2 = 0 + 17.8 Combine like terms: -17.8 + 17.8 = 0.0 0.0 + 0.6x + x2 = 0 + 17.8 0.6x + x2 = 0 + 17.8 Combine like terms: 0 + 17.8 = 17.8 0.6x + x2 = 17.8 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 = 17.8 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 17.8 + 0.09 Combine like terms: 17.8 + 0.09 = 17.89 0.09 + 0.6x + x2 = 17.89 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 17.89 Calculate the square root of the right side: 4.229657197 Break this problem into two subproblems by setting (x + 0.3) equal to 4.229657197 and -4.229657197.Subproblem 1
x + 0.3 = 4.229657197 Simplifying x + 0.3 = 4.229657197 Reorder the terms: 0.3 + x = 4.229657197 Solving 0.3 + x = 4.229657197 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 = 4.229657197 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 4.229657197 + -0.3 x = 4.229657197 + -0.3 Combine like terms: 4.229657197 + -0.3 = 3.929657197 x = 3.929657197 Simplifying x = 3.929657197Subproblem 2
x + 0.3 = -4.229657197 Simplifying x + 0.3 = -4.229657197 Reorder the terms: 0.3 + x = -4.229657197 Solving 0.3 + x = -4.229657197 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 = -4.229657197 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -4.229657197 + -0.3 x = -4.229657197 + -0.3 Combine like terms: -4.229657197 + -0.3 = -4.529657197 x = -4.529657197 Simplifying x = -4.529657197Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.929657197, -4.529657197}
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