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Simplifying 5x2 + 3x = 9 + 15 Reorder the terms: 3x + 5x2 = 9 + 15 Combine like terms: 9 + 15 = 24 3x + 5x2 = 24 Solving 3x + 5x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 3x + 5x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + 0.6x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 0.6x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 0.6x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 0.6x + x2 = 0 + 4.8 0.6x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 0.6x + x2 = 4.8 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 = 4.8 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 4.8 + 0.09 Combine like terms: 4.8 + 0.09 = 4.89 0.09 + 0.6x + x2 = 4.89 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 4.89 Calculate the square root of the right side: 2.211334439 Break this problem into two subproblems by setting (x + 0.3) equal to 2.211334439 and -2.211334439.Subproblem 1
x + 0.3 = 2.211334439 Simplifying x + 0.3 = 2.211334439 Reorder the terms: 0.3 + x = 2.211334439 Solving 0.3 + x = 2.211334439 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 = 2.211334439 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 2.211334439 + -0.3 x = 2.211334439 + -0.3 Combine like terms: 2.211334439 + -0.3 = 1.911334439 x = 1.911334439 Simplifying x = 1.911334439Subproblem 2
x + 0.3 = -2.211334439 Simplifying x + 0.3 = -2.211334439 Reorder the terms: 0.3 + x = -2.211334439 Solving 0.3 + x = -2.211334439 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 = -2.211334439 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -2.211334439 + -0.3 x = -2.211334439 + -0.3 Combine like terms: -2.211334439 + -0.3 = -2.511334439 x = -2.511334439 Simplifying x = -2.511334439Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.911334439, -2.511334439}
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