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Simplifying 43x + 51 = 6(6x + 9) * 7x + -3 Reorder the terms: 51 + 43x = 6(6x + 9) * 7x + -3 Reorder the terms: 51 + 43x = 6(9 + 6x) * 7x + -3 Reorder the terms for easier multiplication: 51 + 43x = 6 * 7x(9 + 6x) + -3 Multiply 6 * 7 51 + 43x = 42x(9 + 6x) + -3 51 + 43x = (9 * 42x + 6x * 42x) + -3 51 + 43x = (378x + 252x2) + -3 Reorder the terms: 51 + 43x = -3 + 378x + 252x2 Solving 51 + 43x = -3 + 378x + 252x2 Solving for variable 'x'. Reorder the terms: 51 + 3 + 43x + -378x + -252x2 = -3 + 378x + 252x2 + 3 + -378x + -252x2 Combine like terms: 51 + 3 = 54 54 + 43x + -378x + -252x2 = -3 + 378x + 252x2 + 3 + -378x + -252x2 Combine like terms: 43x + -378x = -335x 54 + -335x + -252x2 = -3 + 378x + 252x2 + 3 + -378x + -252x2 Reorder the terms: 54 + -335x + -252x2 = -3 + 3 + 378x + -378x + 252x2 + -252x2 Combine like terms: -3 + 3 = 0 54 + -335x + -252x2 = 0 + 378x + -378x + 252x2 + -252x2 54 + -335x + -252x2 = 378x + -378x + 252x2 + -252x2 Combine like terms: 378x + -378x = 0 54 + -335x + -252x2 = 0 + 252x2 + -252x2 54 + -335x + -252x2 = 252x2 + -252x2 Combine like terms: 252x2 + -252x2 = 0 54 + -335x + -252x2 = 0 Begin completing the square. Divide all terms by -252 the coefficient of the squared term: Divide each side by '-252'. -0.2142857143 + 1.329365079x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 1.329365079x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 1.329365079x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 1.329365079x + x2 = 0 + 0.2142857143 1.329365079x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 1.329365079x + x2 = 0.2142857143 The x term is 1.329365079x. Take half its coefficient (0.6646825395). Square it (0.4418028783) and add it to both sides. Add '0.4418028783' to each side of the equation. 1.329365079x + 0.4418028783 + x2 = 0.2142857143 + 0.4418028783 Reorder the terms: 0.4418028783 + 1.329365079x + x2 = 0.2142857143 + 0.4418028783 Combine like terms: 0.2142857143 + 0.4418028783 = 0.6560885926 0.4418028783 + 1.329365079x + x2 = 0.6560885926 Factor a perfect square on the left side: (x + 0.6646825395)(x + 0.6646825395) = 0.6560885926 Calculate the square root of the right side: 0.809992958 Break this problem into two subproblems by setting (x + 0.6646825395) equal to 0.809992958 and -0.809992958.Subproblem 1
x + 0.6646825395 = 0.809992958 Simplifying x + 0.6646825395 = 0.809992958 Reorder the terms: 0.6646825395 + x = 0.809992958 Solving 0.6646825395 + x = 0.809992958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6646825395' to each side of the equation. 0.6646825395 + -0.6646825395 + x = 0.809992958 + -0.6646825395 Combine like terms: 0.6646825395 + -0.6646825395 = 0.0000000000 0.0000000000 + x = 0.809992958 + -0.6646825395 x = 0.809992958 + -0.6646825395 Combine like terms: 0.809992958 + -0.6646825395 = 0.1453104185 x = 0.1453104185 Simplifying x = 0.1453104185Subproblem 2
x + 0.6646825395 = -0.809992958 Simplifying x + 0.6646825395 = -0.809992958 Reorder the terms: 0.6646825395 + x = -0.809992958 Solving 0.6646825395 + x = -0.809992958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6646825395' to each side of the equation. 0.6646825395 + -0.6646825395 + x = -0.809992958 + -0.6646825395 Combine like terms: 0.6646825395 + -0.6646825395 = 0.0000000000 0.0000000000 + x = -0.809992958 + -0.6646825395 x = -0.809992958 + -0.6646825395 Combine like terms: -0.809992958 + -0.6646825395 = -1.4746754975 x = -1.4746754975 Simplifying x = -1.4746754975Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1453104185, -1.4746754975}
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