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Simplifying 5x(5x + 3) = 19 Reorder the terms: 5x(3 + 5x) = 19 (3 * 5x + 5x * 5x) = 19 (15x + 25x2) = 19 Solving 15x + 25x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 15x + 25x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 15x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.76 + 0.6x + x2 = 0 Move the constant term to the right: Add '0.76' to each side of the equation. -0.76 + 0.6x + 0.76 + x2 = 0 + 0.76 Reorder the terms: -0.76 + 0.76 + 0.6x + x2 = 0 + 0.76 Combine like terms: -0.76 + 0.76 = 0.00 0.00 + 0.6x + x2 = 0 + 0.76 0.6x + x2 = 0 + 0.76 Combine like terms: 0 + 0.76 = 0.76 0.6x + x2 = 0.76 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 = 0.76 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.76 + 0.09 Combine like terms: 0.76 + 0.09 = 0.85 0.09 + 0.6x + x2 = 0.85 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.85 Calculate the square root of the right side: 0.921954446 Break this problem into two subproblems by setting (x + 0.3) equal to 0.921954446 and -0.921954446.Subproblem 1
x + 0.3 = 0.921954446 Simplifying x + 0.3 = 0.921954446 Reorder the terms: 0.3 + x = 0.921954446 Solving 0.3 + x = 0.921954446 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 = 0.921954446 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.921954446 + -0.3 x = 0.921954446 + -0.3 Combine like terms: 0.921954446 + -0.3 = 0.621954446 x = 0.621954446 Simplifying x = 0.621954446Subproblem 2
x + 0.3 = -0.921954446 Simplifying x + 0.3 = -0.921954446 Reorder the terms: 0.3 + x = -0.921954446 Solving 0.3 + x = -0.921954446 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 = -0.921954446 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.921954446 + -0.3 x = -0.921954446 + -0.3 Combine like terms: -0.921954446 + -0.3 = -1.221954446 x = -1.221954446 Simplifying x = -1.221954446Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.621954446, -1.221954446}
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