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Simplifying 6.4(x + 4) + 4x2 + 3.4(x + -3) = 54 Reorder the terms: 6.4(4 + x) + 4x2 + 3.4(x + -3) = 54 (4 * 6.4 + x * 6.4) + 4x2 + 3.4(x + -3) = 54 (25.6 + 6.4x) + 4x2 + 3.4(x + -3) = 54 Reorder the terms: 25.6 + 6.4x + 4x2 + 3.4(-3 + x) = 54 25.6 + 6.4x + 4x2 + (-3 * 3.4 + x * 3.4) = 54 25.6 + 6.4x + 4x2 + (-10.2 + 3.4x) = 54 Reorder the terms: 25.6 + -10.2 + 6.4x + 3.4x + 4x2 = 54 Combine like terms: 25.6 + -10.2 = 15.4 15.4 + 6.4x + 3.4x + 4x2 = 54 Combine like terms: 6.4x + 3.4x = 9.8x 15.4 + 9.8x + 4x2 = 54 Solving 15.4 + 9.8x + 4x2 = 54 Solving for variable 'x'. Reorder the terms: 15.4 + -54 + 9.8x + 4x2 = 54 + -54 Combine like terms: 15.4 + -54 = -38.6 -38.6 + 9.8x + 4x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -38.6 + 9.8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.65 + 2.45x + x2 = 0 Move the constant term to the right: Add '9.65' to each side of the equation. -9.65 + 2.45x + 9.65 + x2 = 0 + 9.65 Reorder the terms: -9.65 + 9.65 + 2.45x + x2 = 0 + 9.65 Combine like terms: -9.65 + 9.65 = 0.00 0.00 + 2.45x + x2 = 0 + 9.65 2.45x + x2 = 0 + 9.65 Combine like terms: 0 + 9.65 = 9.65 2.45x + x2 = 9.65 The x term is 2.45x. Take half its coefficient (1.225). Square it (1.500625) and add it to both sides. Add '1.500625' to each side of the equation. 2.45x + 1.500625 + x2 = 9.65 + 1.500625 Reorder the terms: 1.500625 + 2.45x + x2 = 9.65 + 1.500625 Combine like terms: 9.65 + 1.500625 = 11.150625 1.500625 + 2.45x + x2 = 11.150625 Factor a perfect square on the left side: (x + 1.225)(x + 1.225) = 11.150625 Calculate the square root of the right side: 3.339255156 Break this problem into two subproblems by setting (x + 1.225) equal to 3.339255156 and -3.339255156.Subproblem 1
x + 1.225 = 3.339255156 Simplifying x + 1.225 = 3.339255156 Reorder the terms: 1.225 + x = 3.339255156 Solving 1.225 + x = 3.339255156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.225' to each side of the equation. 1.225 + -1.225 + x = 3.339255156 + -1.225 Combine like terms: 1.225 + -1.225 = 0.000 0.000 + x = 3.339255156 + -1.225 x = 3.339255156 + -1.225 Combine like terms: 3.339255156 + -1.225 = 2.114255156 x = 2.114255156 Simplifying x = 2.114255156Subproblem 2
x + 1.225 = -3.339255156 Simplifying x + 1.225 = -3.339255156 Reorder the terms: 1.225 + x = -3.339255156 Solving 1.225 + x = -3.339255156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.225' to each side of the equation. 1.225 + -1.225 + x = -3.339255156 + -1.225 Combine like terms: 1.225 + -1.225 = 0.000 0.000 + x = -3.339255156 + -1.225 x = -3.339255156 + -1.225 Combine like terms: -3.339255156 + -1.225 = -4.564255156 x = -4.564255156 Simplifying x = -4.564255156Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.114255156, -4.564255156}
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