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Simplifying 5.2x(2x + 4) = 30 Reorder the terms: 5.2x(4 + 2x) = 30 (4 * 5.2x + 2x * 5.2x) = 30 (20.8x + 10.4x2) = 30 Solving 20.8x + 10.4x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 20.8x + 10.4x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 20.8x + 10.4x2 = 0 Begin completing the square. Divide all terms by 10.4 the coefficient of the squared term: Divide each side by '10.4'. -2.884615385 + 2x + x2 = 0 Move the constant term to the right: Add '2.884615385' to each side of the equation. -2.884615385 + 2x + 2.884615385 + x2 = 0 + 2.884615385 Reorder the terms: -2.884615385 + 2.884615385 + 2x + x2 = 0 + 2.884615385 Combine like terms: -2.884615385 + 2.884615385 = 0.000000000 0.000000000 + 2x + x2 = 0 + 2.884615385 2x + x2 = 0 + 2.884615385 Combine like terms: 0 + 2.884615385 = 2.884615385 2x + x2 = 2.884615385 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 2.884615385 + 1 Reorder the terms: 1 + 2x + x2 = 2.884615385 + 1 Combine like terms: 2.884615385 + 1 = 3.884615385 1 + 2x + x2 = 3.884615385 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.884615385 Calculate the square root of the right side: 1.970942766 Break this problem into two subproblems by setting (x + 1) equal to 1.970942766 and -1.970942766.Subproblem 1
x + 1 = 1.970942766 Simplifying x + 1 = 1.970942766 Reorder the terms: 1 + x = 1.970942766 Solving 1 + x = 1.970942766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.970942766 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.970942766 + -1 x = 1.970942766 + -1 Combine like terms: 1.970942766 + -1 = 0.970942766 x = 0.970942766 Simplifying x = 0.970942766Subproblem 2
x + 1 = -1.970942766 Simplifying x + 1 = -1.970942766 Reorder the terms: 1 + x = -1.970942766 Solving 1 + x = -1.970942766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.970942766 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.970942766 + -1 x = -1.970942766 + -1 Combine like terms: -1.970942766 + -1 = -2.970942766 x = -2.970942766 Simplifying x = -2.970942766Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.970942766, -2.970942766}
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