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Simplifying 2x(4 + 5x) = 45 (4 * 2x + 5x * 2x) = 45 (8x + 10x2) = 45 Solving 8x + 10x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 8x + 10x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 8x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -4.5 + 0.8x + x2 = 0.0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 0.8x + 4.5 + x2 = 0.0 + 4.5 Reorder the terms: -4.5 + 4.5 + 0.8x + x2 = 0.0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 0.8x + x2 = 0.0 + 4.5 0.8x + x2 = 0.0 + 4.5 Combine like terms: 0.0 + 4.5 = 4.5 0.8x + x2 = 4.5 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 4.5 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 4.5 + 0.16 Combine like terms: 4.5 + 0.16 = 4.66 0.16 + 0.8x + x2 = 4.66 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 4.66 Calculate the square root of the right side: 2.158703314 Break this problem into two subproblems by setting (x + 0.4) equal to 2.158703314 and -2.158703314.Subproblem 1
x + 0.4 = 2.158703314 Simplifying x + 0.4 = 2.158703314 Reorder the terms: 0.4 + x = 2.158703314 Solving 0.4 + x = 2.158703314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.158703314 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.158703314 + -0.4 x = 2.158703314 + -0.4 Combine like terms: 2.158703314 + -0.4 = 1.758703314 x = 1.758703314 Simplifying x = 1.758703314Subproblem 2
x + 0.4 = -2.158703314 Simplifying x + 0.4 = -2.158703314 Reorder the terms: 0.4 + x = -2.158703314 Solving 0.4 + x = -2.158703314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.158703314 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.158703314 + -0.4 x = -2.158703314 + -0.4 Combine like terms: -2.158703314 + -0.4 = -2.558703314 x = -2.558703314 Simplifying x = -2.558703314Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.758703314, -2.558703314}
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