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Simplifying 4x2 + 4.65x = 0.65 Reorder the terms: 4.65x + 4x2 = 0.65 Solving 4.65x + 4x2 = 0.65 Solving for variable 'x'. Reorder the terms: -0.65 + 4.65x + 4x2 = 0.65 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 -0.65 + 4.65x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.1625 + 1.1625x + x2 = 0.00 Move the constant term to the right: Add '0.1625' to each side of the equation. -0.1625 + 1.1625x + 0.1625 + x2 = 0.00 + 0.1625 Reorder the terms: -0.1625 + 0.1625 + 1.1625x + x2 = 0.00 + 0.1625 Combine like terms: -0.1625 + 0.1625 = 0.0000 0.0000 + 1.1625x + x2 = 0.00 + 0.1625 1.1625x + x2 = 0.00 + 0.1625 Combine like terms: 0.00 + 0.1625 = 0.1625 1.1625x + x2 = 0.1625 The x term is 1.1625x. Take half its coefficient (0.58125). Square it (0.3378515625) and add it to both sides. Add '0.3378515625' to each side of the equation. 1.1625x + 0.3378515625 + x2 = 0.1625 + 0.3378515625 Reorder the terms: 0.3378515625 + 1.1625x + x2 = 0.1625 + 0.3378515625 Combine like terms: 0.1625 + 0.3378515625 = 0.5003515625 0.3378515625 + 1.1625x + x2 = 0.5003515625 Factor a perfect square on the left side: (x + 0.58125)(x + 0.58125) = 0.5003515625 Calculate the square root of the right side: 0.70735533 Break this problem into two subproblems by setting (x + 0.58125) equal to 0.70735533 and -0.70735533.Subproblem 1
x + 0.58125 = 0.70735533 Simplifying x + 0.58125 = 0.70735533 Reorder the terms: 0.58125 + x = 0.70735533 Solving 0.58125 + x = 0.70735533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.58125' to each side of the equation. 0.58125 + -0.58125 + x = 0.70735533 + -0.58125 Combine like terms: 0.58125 + -0.58125 = 0.00000 0.00000 + x = 0.70735533 + -0.58125 x = 0.70735533 + -0.58125 Combine like terms: 0.70735533 + -0.58125 = 0.12610533 x = 0.12610533 Simplifying x = 0.12610533Subproblem 2
x + 0.58125 = -0.70735533 Simplifying x + 0.58125 = -0.70735533 Reorder the terms: 0.58125 + x = -0.70735533 Solving 0.58125 + x = -0.70735533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.58125' to each side of the equation. 0.58125 + -0.58125 + x = -0.70735533 + -0.58125 Combine like terms: 0.58125 + -0.58125 = 0.00000 0.00000 + x = -0.70735533 + -0.58125 x = -0.70735533 + -0.58125 Combine like terms: -0.70735533 + -0.58125 = -1.28860533 x = -1.28860533 Simplifying x = -1.28860533Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12610533, -1.28860533}
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